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currently I'm using Krylov's book, while consulting Evans (too many details are left out, for my level).

Also, Adams 1975 version has been widely cited.

So besides these ones, which book in your mind would be best for using as a reference that provides complete treatment on Sobolev topics?

Cheers.

P.S: please feel free to move this topic to wiki cite, if necessary.

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    Different from Krylov's and Evans' for sure, since these two are PDE books, not Sobolev spaces books. If you like the functional analysis emphasis (interpolation etc), then Adams is the way to go. I prefer calculus to functional analysis, so for me Leoni works better. I also benefited from *Measure Theory...* by Evans and Gariepy, and, to a lesser degree, from *Weakly differentiable functions* by Ziemer. Ultimately, it depends on what you want to learn about Sobolev spaces2012-06-01

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Compiling the suggestions:

  • A First Course on Sobolev Spaces by Giovanni Leoni (user-friendly exposition rooted in calculus)
  • Measure Theory and Fine Properties of Functions by Evans and Gariepy (not exclusively about Sobolev spaces, but covers the most essential results)
  • Weakly differentiable functions by Ziemer (emphasis on BV)

And adding one more:

  • Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis: a widely used book oriented at functional analysis methods in PDE. Lots of exercises.