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

Authors

  • Stahn Reinhard Institut fur Analysis, Technische Universit¨at Dresden Germany, 01062, Dresden, Helmholtzstr., 10

Abstract

We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set Ω. We make no assumptions about the open set Ω and very mild regularity assumptions on the semilinearity f, plus a coerciveness assumption which depends on the optimal Poincar´e-Steklov constant λ1. 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. Refs 17.

Keywords:

elliptic, semilinear, locally convex, fixed point, arbitrary domain

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Published

2015-11-01

How to Cite

Reinhard, S. (2015). Existence of solutions for semilinear elliptic boundary value problems on arbitrary open sets. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(4), 576–588. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11193

Issue

Vol. 2 No. 4 (2015)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.