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arXiv · 2005.10941

Improved regularity for the $p$-Poisson equation

Edgard A. Pimentel·Giane C. Rampasso·Makson S. Santos
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Abstract

In this paper we produce new, optimal, regularity results for the solutions to $p$-Poisson equations. We argue through a delicate approximation method, under a smallness regime for the exponent $p$, that imports information from a limiting profile driven by the Laplace operator. Our arguments contain a novelty of technical interest, namely a sequential stability result; it connects the solutions to $p$-Poisson equations with harmonic functions, yielding improved regularity for the former. Our findings relate a smallness regime with improved $\mathcal{C}^{1,1-}$-estimates in the presence of $L^\infty$-source terms.

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Edgard A. Pimentel, Giane C. Rampasso, Makson S. Santos. 2020-05-21. Improved regularity for the $p$-Poisson equation. https://doi.org/10.1088/1361-6544/ab7d21

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