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Peer-reviewedCC BY 4.0Axioms

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

  • Xingyue He1
  • Jingjing Wang1
  1. 1School of Information Engineering, Lanzhou City University, Lanzhou 730070, China
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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.

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Cite

BibTeXRIS
BibTeX
@article{he2026boundary,
  title = {{Boundary Hölder Regularity of a Class of Monge–Ampère Equations at Some Special Points}},
  author = {Xingyue He and Jingjing Wang},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15110791},
  url = {https://www.mdpi.com/2075-1680/15/11/791},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Boundary Hölder Regularity of a Class of Monge–Ampère Equations at Some Special Points
AU  - Xingyue He
AU  - Jingjing Wang
PY  - 2026
DA  - 2026/10/22
JO  - Axioms
DO  - 10.3390/axioms15110791
UR  - https://www.mdpi.com/2075-1680/15/11/791
AB  - 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.
SN  - 2075-1680
ER  -