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arXiv · 2003.07084

A mean value formula for the variational $p$-Laplacian

Félix del Teso·Erik Lindgren
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Abstract

We prove a new asymptotic mean value formula for the $p$-Laplace operator, $$ \Delta_p u=\text{div}(|\nabla u|^{p-2}\nabla u), $$ valid in the viscosity sense. In the plane, and for a certain range of $p$, the mean value formula holds in the pointwise sense. We also study the existence, uniqueness and convergence of the related dynamic programming principle.

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Félix del Teso, Erik Lindgren. 2020-03-16. A mean value formula for the variational $p$-Laplacian. https://arxiv.org/abs/2003.07084

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