Detail publikace

Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

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

Originální název

Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

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

Vydáno

6. 6. 2025

ISSN

0944-2669

Periodikum

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Ročník

64

Číslo

5

Stát

Spojené státy americké

Strany počet

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"
}