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1 vote

Derive elliptic maximum principle from weak derivatives

This is not a complete answer. Since $u-\sup_{\partial U} u$ solves the same inequation, w.l.o.g. you can assume that $ u\leq 0$ on $\partial U$ and you want to prove $u\leq 0$ inside. By density your ...
Ayman Moussa's user avatar
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2 votes
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Well posedness of the Plateau problem under lack of uniqueness

I am far from being an expert, but if I understand your question correctly, the answer is "no", at least for the Plateau problem in the realm of Caccioppoli sets. Vinti's cited result [2] ...
Michele Caselli's user avatar
3 votes
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On the weak derivative of $|u|^{(p-2)/2}u$

Only a partial answer : (2) seems strange. In dimension $1$, if $u$ does not change sign, your setting includes the one of $u^\alpha \in H^1(0,1)$ (boundary values are irrelevant here) for some $\...
Ayman Moussa's user avatar
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6 votes
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Uniqueness of constructed solutions to the Helmholtz equation

The old Sherlock Holmes adage When you have eliminated the impossible, whatever remains, however improbable, must be the truth. applies here. Since nothing else you did was wrong, it must be your ...
Willie Wong's user avatar
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