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• W3006807158 abstract "We study the problem of finding a function u verifying --$Delta$u = 0 in $Omega$ under the boundary condition $partial$u $partial$n + g(u) = $mu$ on $partial$$Omega$ where $Omega$ $subset$ R N is a smooth domain, n the normal unit outward vector to $Omega$, $mu$ is a measure on $partial$$Omega$ and g a continuous nondecreasing function. We give sufficient condition on g for this problem to be solvable for any measure. When g(r) = |r| p--1 r, p > 1, we give conditions in order an isolated singularity on $partial$$Omega$ be removable. We also give capacitary conditions on a measure $mu$ in order the problem with g(r) = |r| p--1 r to be solvable for some $mu$. We also study the isolated singularities of functions satisfying --$Delta$u = 0 in $Omega$ and $partial$u $partial$n + g(u) = 0 on $partial$$Omega$ {0}." @default.
• W3006807158 created "2020-03-06" @default.
• W3006807158 creator A5036556016 @default.
• W3006807158 creator A5072943755 @default.
• W3006807158 date "2020-03-02" @default.
• W3006807158 modified "2023-09-26" @default.
• W3006807158 title "Nonlinear boundary value problems relative to harmonic functions." @default.
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• W3006807158 hasPublicationYear "2020" @default.
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