Global H\"{o}lder solvability of linear and quasilinear Poisson equations

Takanobu Hara

Nov 2023

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We discuss the homogeneous Dirichlet problem for $p$-Poisson type equations with locally finite measure data. If there is a H\"{o}lder continuous solution, the corresponding data satisfies a local Morrey type condition. The main result of this paper provides existence of a global H\"{o}lder continuous solution under the same condition. The existence result gives a compact embedding theorem. Our results are also new even for the Poisson equation.

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