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arXiv · 1507.08846

Existence of solutions for semilinear elliptic boundary value problems on arbitrary open sets

Reinhard Stahn
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Abstract

We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set. We make no assumptions about the open set, very mild regularity assumptions on the semilinearity, plus a coerciveness assumption which depends on the optimal Poincare-Steklov constant. The proof is based on Schaefer's fixed point theorem applied to a sequence of truncated problems. We state a simple uniqueness result. We also generalize the results to Robin boundary conditions.

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Reinhard Stahn. 2015-07-31. Existence of solutions for semilinear elliptic boundary value problems on arbitrary open sets. https://doi.org/10.3103/s1063454115040123

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