Concavity of solutions to semilinear equations in dimension two
Analysis of PDEs
2024-12-16 v1
Abstract
We consider the Dirichlet problem for a class of semilinear equations on two dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions.
Keywords
Cite
@article{arxiv.2204.02384,
title = {Concavity of solutions to semilinear equations in dimension two},
author = {Albert Chau and Ben Weinkove},
journal= {arXiv preprint arXiv:2204.02384},
year = {2024}
}
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11 pages