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arXiv · 1903.08676

Parabolic Minkowski convolutions of viscosity solutions to fully nonlinear equations

Kazuhiro Ishige·Qing Liu·Paolo Salani
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Abstract

This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of initial-boundary value problems in different domains. As a consequence, we can for instance obtain parabolic power concavity of solutions to a general class of parabolic equations. Our results apply to the Pucci operator, the normalized $q$-Laplacians with $1<q\leq\infty$, the Finsler Laplacian and more general quasilinear operators.

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Kazuhiro Ishige, Qing Liu, Paolo Salani. 2019-03-20. Parabolic Minkowski convolutions of viscosity solutions to fully nonlinear equations. https://arxiv.org/abs/1903.08676

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