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arXiv · 2204.02384

Concavity of solutions to semilinear equations in dimension two

Albert Chau·Ben Weinkove
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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.

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Albert Chau, Ben Weinkove. 2022-04-05. Concavity of solutions to semilinear equations in dimension two. https://arxiv.org/abs/2204.02384

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