I'm looking for a comprehensive reference illustrating, from the ground up, the basics of weighted Sobolev Spaces on Lipschitz domains (this case should be included, but I don't need less than it). Possibly, application to elliptic PDEs are also sketched. Do you know of any good source for this?
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$\begingroup$ Speaking as a researcher and teacher of functional analysis, it is not clear what "from the ground up" means. Can we assume familiarity with the definition of a Hilbert space? Distribution theory in the sense of Schwartz? Rellich's lemma? If not, where do you want this reference to start from, in terms of prerequisite knowledge? $\endgroup$– Yemon ChoiCommented May 26, 2022 at 20:30
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1$\begingroup$ @YemonChoi I would consider a basic course in functional analysis and PDE's/Sobolev spaces the prerequisite knowledge I'm looking for. Thank you. Personally, I am not familiar with Rellich's lemma, medium familiar with distributions, familiar with Hilbert spaces. $\endgroup$– LillaCommented May 26, 2022 at 21:03
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$\begingroup$ Thanks for the clarification. I don't work much with Sobolev spaces/PDE and tend to be self-taught in the small amount that I need, so I don't know first hand of a good reference. I assume you've tried Adams's book Sobolev Spaces which gets quoted as a standard reference? $\endgroup$– Yemon ChoiCommented May 26, 2022 at 22:12
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1$\begingroup$ @YemonChoi Yes, nothing is mentioned there... $\endgroup$– LillaCommented May 27, 2022 at 8:15
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