Year: 2026
Type: preprint
Abstract: We establish necessary and sufficient conditions for global Hölder solvability of weighted Poisson equations and related fractional problems. On domains satisfying a capacity density condition, a nonnegative measure with bounded support depth admits a bounded globally Hölder continuous zero-boundary solution if and only if it satisfies an interior Morrey-type growth condition. Conversely, uniform boundary decay estimates for solutions with localized nonnegative sources characterize the capacity density condition. Analogous characterizations are established for the restricted and spectral fractional Laplacians. Our approach is based on weighted strong barriers and also yields two-weight Hardy inequalities, compact trace embeddings, and global Hölder solvability for nonlinear Dirichlet-to-Neumann operators.
Source: arXiv (Cornell University)
Author: Hara, Takanobu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223702296