DOI: 10.3390/axioms15110791 ISSN: 2075-1680

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

Xingyue He, Jingjing Wang
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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.

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