We present a nonvariational setting for the Neumann problem for the Poisson equation for solutions that are Hölder 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 which 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.
A nonvariational form of the Neumann problem for the Poisson equation
Lanza de Cristoforis, M.
2026
Abstract
We present a nonvariational setting for the Neumann problem for the Poisson equation for solutions that are Hölder 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 which 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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