Global H\"{o}lder solvability of second order elliptic equations with locally integrable lower-order coefficients
Analysis of PDEs
2025-05-27 v2
Abstract
We prove the existence of globally H\"{o}lder continuous solutions to certain elliptic partial differential equations with lower-order terms. Our result is applicable to coefficients controlled by a negative power of the distance from the boundary of the domain and significantly improves Theorem 8.30 in Gilbarg and Trudinger (1983). The proof is derived by applying the strategy of Ancona (1986) to a new Morrey-type space.
Keywords
Cite
@article{arxiv.2403.01104,
title = {Global H\"{o}lder solvability of second order elliptic equations with locally integrable lower-order coefficients},
author = {Takanobu Hara},
journal= {arXiv preprint arXiv:2403.01104},
year = {2025}
}
Comments
This is the author's accepted manuscript. First published in Proceedings of the American Mathematical Society in (2025), published by the American Mathematical Society