Szczegóły publikacji
Opis bibliograficzny
Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations / Yuzhou Fang, Vicenţiu D. RĂDULESCU, Chao Zhang // Calculus of Variations and Partial Differential Equations ; ISSN 0944-2669. — 2025 — vol. 64 iss. 5 art. no. 159, s. 1-29. — Bibliogr. s. 27-29, Abstr. — Publikacja dostępna online od: 2025-05-27. — V. D. Rǎdulescu - dod. afiliacje: Department of Mathematics, University of Craiova, Romania; Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania; Faculty of Electrical Engineering and Communication, Brno University of Technology, Czech Republic; School of Mathematics, Zhejiang Normal University, Jinhua, China
Autorzy (3)
- Fang Yuzhou
- AGHRǎdulescu Vicenţiu
- Zhang Chao
Dane bibliometryczne
| ID BaDAP | 162244 |
|---|---|
| Data dodania do BaDAP | 2025-09-11 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s00526-025-03023-4 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Calculus of Variations and Partial Differential Equations |
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 H & ouml;lder 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,alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>{1, \alpha }_\textrm{loc}$$\end{document}. Additionally, if the order of the fractional diffusion is in the interval (0, 1], the local H & ouml;lder continuity of solutions is inferred.
