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On a nonlinear elliptic boundary value problem


Author: Nguyên Phuong Các
Journal: Proc. Amer. Math. Soc. 50 (1975), 230-236
MSC: Primary 35J65
DOI: https://doi.org/10.1090/S0002-9939-1975-0369911-5
MathSciNet review: 0369911
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Abstract: Consider a bounded domain $ G \subset {R^N}(N \geq 1)$ with smooth boundary $ \Gamma $. Let $ L$ be a uniformly elliptic linear differential operator. Let $ \gamma $ and $ \beta $ be two maximal monotone mappings in $ R$. We prove that, when $ \gamma $ satisfies a certain growth condition, given $ f \in {L^2}(G)$ there is $ u \in {H^2}(G)$ such that

$\displaystyle Lu + \gamma (u) \mathrel\backepsilon f\quad {\text{a.}}{\text{e.}... ...\in \beta ({u_{\vert\Gamma }})\quad {\text{a.}}{\text{e.}}{\text{ on }}\Gamma ,$

where $ \partial u/\partial v$ is the conormal derivative associated with $ L$.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0369911-5
Keywords: Maximal monotone operators, Yosida approximation, nonlinear elliptic boundary value problem
Article copyright: © Copyright 1975 American Mathematical Society

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