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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

1 vote
0 answers
173 views

Regularity of weak solution

I have also posted the question here. Let me explain what difficulties I have. In fact, one may write \begin{equation} \partial_1(f-\partial_1 u)=0 \end{equation} in $\Omega$. Then one may have the fo …
Peter's user avatar
  • 223
2 votes
0 answers
152 views

Browder's Fixed Point Theorem in uniformly convex Banach spaces with non-identical image

This is in fact an exercise from Dirk Werner's book "Funktionalanalysis", but I do think that the result is quite interesting and up to now, I can only partly solve this problem. From the point of my …
Peter's user avatar
  • 223