Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities
Analysis of PDEs
2017-11-27 v1 Differential Geometry
Abstract
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian manifolds. As a byproduct of the proofs we also obtain some rigidity, or partial symmetry, results for solutions to overdetermined problems on Riemannian manifolds of nonconstant curvature.
Keywords
Cite
@article{arxiv.1711.08649,
title = {Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities},
author = {Miguel Dominguez-Vazquez and Alberto Enciso and Daniel Peralta-Salas},
journal= {arXiv preprint arXiv:1711.08649},
year = {2017}
}
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36 pages