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arXiv · 2209.03194

Wulff shape symmetry of solutions to overdetermined problems for Finsler Monge-Amp\`ere equations

Andrea Cianchi·Paolo Salani
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Abstract

We deal with Monge-Amp\`ere type equations modeled upon general anisotropic norms $H$ in $\mathbb R^n$. An overdetermined problem for convex solutions to these equations is analyzed. The relevant solutions are subject to both a homogeneous Dirichlet condition and a second boundary condition, designed on $H$, on the gradient image of the domain. The Wulff shape symmetry associated with $H$ of the solutions is established.

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Andrea Cianchi, Paolo Salani. 2022-09-07. Wulff shape symmetry of solutions to overdetermined problems for Finsler Monge-Amp\`ere equations. https://arxiv.org/abs/2209.03194

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