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arXiv · 2405.01818

A nonvariational form of the Neumann problem for the Poisson equation

M. Lanza de Cristoforis
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Abstract

We present a nonvariational setting for the Neumann problem for the Poisson equation for solutions that are H\"{o}lder continuous and that may have infinite Dirichlet integral. We introduce a distributional normal derivative on the boundary for the solutions that extends that for harmonic functions that has been introduced in a previous paper and we solve the nonvariational Neumann problem for data in the interior with a negative Schauder exponent and for data on the boundary that belong to a certain space of distributions on the boundary.

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M. Lanza de Cristoforis. 2024-05-03. A nonvariational form of the Neumann problem for the Poisson equation. https://arxiv.org/abs/2405.01818

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