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arXiv · 2010.13945

Overdetermined problems for fully nonlinear equations in space forms

Ignace Aristide Minlend
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Abstract

We study overdetermined problems for fully nonlinear elliptic equations in subdomains $\O$ of the Euclidean sphere $\mathbb{S}^{N}$ and the hyperbolic space $\mathbb{H}^{N}$. We prove, the existence of a classical solution to the underlined equation forces $\O$ to be a geodesic ball in the ambient space. Our result extends to fully nonlinear equations, a similar result in the case of semilinear equations with the Laplace operator due to Kumaresan and Prajapat.

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Ignace Aristide Minlend. 2020-10-26. Overdetermined problems for fully nonlinear equations in space forms. https://arxiv.org/abs/2010.13945

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