Work

Global Hölder solvability of second order elliptic equations with locally integrable lower-order coefficients

Year: 2025

Type: article

Abstract: We prove the existence of globally Hölder 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 [ Elliptic partial differential equations of second order , Classics in Mathematics, Springer-Verlag, Berlin, 2001]. The proof is derived by applying the strategy of Ancona [J. London Math. Soc. (2) 34 (1986), pp. 274–290] to a new Morrey-type space.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17331

Author: Takanobu Hara

Institution: Tohoku University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Japan Society for the Promotion of Science, Research Institute for Mathematical Sciences, Division of Mathematical Sciences, Core Research for Evolutional Science and Technology