Textbook recommendation request: Exercises to supplement Evans and Gariepy












7












$begingroup$


While a great book about measure theory and real analysis in $mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it for self study.






real-analysis geometric-measure-theory textbook-recommendation







share|cite|improve this question









$endgroup$












  • $begingroup$
    Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
    $endgroup$
    – Y.B.
    2 days ago










  • $begingroup$
    Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
    $endgroup$
    – Y.B.
    2 days ago










  • $begingroup$
    I will check out the first one, seems interesting!
    $endgroup$
    – James Baxter
    2 days ago






  • 1




    $begingroup$
    This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
    $endgroup$
    – Piotr Hajlasz
    2 days ago
















7












$begingroup$


While a great book about measure theory and real analysis in $mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it for self study.






real-analysis geometric-measure-theory textbook-recommendation







share|cite|improve this question









$endgroup$












  • $begingroup$
    Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
    $endgroup$
    – Y.B.
    2 days ago










  • $begingroup$
    Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
    $endgroup$
    – Y.B.
    2 days ago










  • $begingroup$
    I will check out the first one, seems interesting!
    $endgroup$
    – James Baxter
    2 days ago






  • 1




    $begingroup$
    This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
    $endgroup$
    – Piotr Hajlasz
    2 days ago














7












7








7


3



$begingroup$


While a great book about measure theory and real analysis in $mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it for self study.






real-analysis geometric-measure-theory textbook-recommendation







share|cite|improve this question









$endgroup$




While a great book about measure theory and real analysis in $mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it for self study.






real-analysis geometric-measure-theory textbook-recommendation




real-analysis geometric-measure-theory textbook-recommendation






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 2 days ago









James BaxterJames Baxter

33313




33313












  • $begingroup$
    Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
    $endgroup$
    – Y.B.
    2 days ago










  • $begingroup$
    Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
    $endgroup$
    – Y.B.
    2 days ago










  • $begingroup$
    I will check out the first one, seems interesting!
    $endgroup$
    – James Baxter
    2 days ago






  • 1




    $begingroup$
    This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
    $endgroup$
    – Piotr Hajlasz
    2 days ago


















  • $begingroup$
    Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
    $endgroup$
    – Y.B.
    2 days ago










  • $begingroup$
    Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
    $endgroup$
    – Y.B.
    2 days ago










  • $begingroup$
    I will check out the first one, seems interesting!
    $endgroup$
    – James Baxter
    2 days ago






  • 1




    $begingroup$
    This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
    $endgroup$
    – Piotr Hajlasz
    2 days ago
















$begingroup$
Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
$endgroup$
– Y.B.
2 days ago




$begingroup$
Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
$endgroup$
– Y.B.
2 days ago












$begingroup$
Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
$endgroup$
– Y.B.
2 days ago




$begingroup$
Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
$endgroup$
– Y.B.
2 days ago












$begingroup$
I will check out the first one, seems interesting!
$endgroup$
– James Baxter
2 days ago




$begingroup$
I will check out the first one, seems interesting!
$endgroup$
– James Baxter
2 days ago




1




1




$begingroup$
This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
$endgroup$
– Piotr Hajlasz
2 days ago




$begingroup$
This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
$endgroup$
– Piotr Hajlasz
2 days ago










2 Answers
2






active

oldest

votes


















5












$begingroup$

If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions Springer 1989



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    2 days ago



















2












$begingroup$

Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    2 days ago










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    2 days ago











Your Answer





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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









5












$begingroup$

If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions Springer 1989



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    2 days ago
















5












$begingroup$

If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions Springer 1989



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    2 days ago














5












5








5





$begingroup$

If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions Springer 1989



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.






share|cite|improve this answer











$endgroup$



If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions Springer 1989



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 2 days ago









Martin Sleziak

2,96532028




2,96532028










answered 2 days ago









Piotr HajlaszPiotr Hajlasz

6,80642457




6,80642457








  • 1




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    2 days ago














  • 1




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    2 days ago








1




1




$begingroup$
What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
$endgroup$
– Y.B.
2 days ago




$begingroup$
What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
$endgroup$
– Y.B.
2 days ago











2












$begingroup$

Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    2 days ago










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    2 days ago
















2












$begingroup$

Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    2 days ago










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    2 days ago














2












2








2





$begingroup$

Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.






share|cite|improve this answer











$endgroup$



Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 2 days ago

























answered 2 days ago









Y.B.Y.B.

11112




11112












  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    2 days ago










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    2 days ago


















  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    2 days ago










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    2 days ago
















$begingroup$
Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
$endgroup$
– Piotr Hajlasz
2 days ago




$begingroup$
Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
$endgroup$
– Piotr Hajlasz
2 days ago












$begingroup$
@PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
$endgroup$
– Y.B.
2 days ago




$begingroup$
@PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
$endgroup$
– Y.B.
2 days ago


















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