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arXiv · 2005.13615

Extremals in nonlinear potential theory

Ryan Hynd·Francis Seuffert
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Abstract

We consider the PDE $-\Delta_pu=\rho$, where $\rho$ is a signed Borel measure on $\mathbb{R}^n$. For each $p>n$, we characterize solutions as extremals of a generalized Morrey inequality determined by $\rho$.

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Ryan Hynd, Francis Seuffert. 2020-05-27. Extremals in nonlinear potential theory. https://arxiv.org/abs/2005.13615

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