Work

Boundary Hölder Regularity of a Class of Monge–Ampère Equations at Some Special Points

Year: 2026

Type: article

Abstract: In this paper, we aim to investigate the boundary Hölder regularity for a class of Monge–Ampère-type equations in a bounded convex domain. We study the local regularity of convex solutions at special (a,η)-type boundary points. By constructing appropriate auxiliary functions and sub-solutions, we investigate the local regularity of convex solutions at some special points, which are called (a,η)-type points. It is emphasized that the regularity of the solution at the boundary depends essentially on the convexity of the domain, and is independent of the smoothness of the domain.

Source: Axioms

DOI: 10.3390/axioms15110791

Authors: Xingyue He, Jingjing Wang

Institution: Lanzhou City University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Lanzhou City University