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• W3100537449 abstract "We prove that for every $p > 1$ and for every potential $V in L^p$, any nonnegative function satisfying $-Delta u + V u ge 0$ in an open connected set of $mathbb{R}^N$ is either identically zero or its level set ${u = 0}$ has zero $W^{2, p}$ capacity. This gives an affirmative answer to an open problem of B'enilan and Brezis concerning a bridge between Serrin-Stampacchia's strong maximum principle for $p > frac{N}{2}$ and Ancona's strong maximum principle for $p = 1$. The proof is based on the construction of suitable test functions depending on the level set ${u = 0}$ and on the existence of solutions of the Dirichlet problem for the Schrodinger operator with diffuse measure data." @default.
• W3100537449 created "2020-11-23" @default.
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• W3100537449 date "2016-04-01" @default.
• W3100537449 modified "2023-09-27" @default.
• W3100537449 title "Strong maximum principle for Schrödinger operators with singular potential" @default.
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• W3100537449 doi "https://doi.org/10.1016/j.anihpc.2014.11.004" @default.
• W3100537449 hasPublicationYear "2016" @default.
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