Publication detail

Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

FANG, Y. RADULESCU, V. ZHANG, C.

Original Title

Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

Type

journal article in Web of Science

Language

English

Original Abstract

We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of viscosity solutions according to different diffusion orders. More precisely, when the order of the fractional diffusion is sufficiently close to 2, we obtain Hölder continuity for the gradient of any viscosity solutions and further derive an improved gradient regularity estimate at the origin. For the order of the fractional diffusion in the interval (1, 2), we prove that there is at least one solution of class Cloc1,α. Additionally, if the order of the fractional diffusion is in the interval (0, 1], the local Hölder continuity of solutions is inferred.

Keywords

INTEGRODIFFERENTIAL EQUATIONS; VISCOSITY SOLUTIONS; MAXIMUM PRINCIPLE; HOLDER CONTINUITY; INTERIOR

Authors

FANG, Y.; RADULESCU, V.; ZHANG, C.

Released

6. 6. 2025

ISBN

0944-2669

Periodical

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Year of study

64

Number

5

State

United States of America

Pages count

29

URL

https://link.springer.com/article/10.1007/s00526-025-03023-4

BibTex

@article{BUT198077,
  author="Yuzhou {Fang} and Vicentiu {Radulescu} and Chao {Zhang}",
  title="Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations",
  journal="CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS",
  year="2025",
  volume="64",
  number="5",
  pages="29",
  doi="10.1007/s00526-025-03023-4",
  issn="0944-2669",
  url="https://link.springer.com/article/10.1007/s00526-025-03023-4"
}