Cordes-Nirenberg type results for nonlocal equations with deforming kernels

Disson dos Prazeres; Aelson Sobral; José Miguel Urbano

doi:10.1016/j.jfa.2024.110593

Cordes-Nirenberg type results for nonlocal equations with deforming kernels

Disson dos Prazeres, Aelson Sobral, José Miguel Urbano^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We derive Cordes-Nirenberg type results for nonlocal elliptic integro-differential equations with deforming kernels comparable to sections of a convex solution of a Monge-Ampère equation. Under a natural integrability assumption on the Monge-Ampère solution, we prove a stability lemma allowing the ellipticity class to vary. Using a compactness method, we then derive Hölder regularity estimates for the gradient of the solutions.

Original language	English (US)
Article number	110593
Journal	Journal of Functional Analysis
Volume	287
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2024.110593
State	Published - Nov 1 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

Deforming kernels
Integro-differential equations
Monge-Ampère equation
Nonlocal elliptic equations

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2024.110593

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title = "Cordes-Nirenberg type results for nonlocal equations with deforming kernels",

abstract = "We derive Cordes-Nirenberg type results for nonlocal elliptic integro-differential equations with deforming kernels comparable to sections of a convex solution of a Monge-Amp{\`e}re equation. Under a natural integrability assumption on the Monge-Amp{\`e}re solution, we prove a stability lemma allowing the ellipticity class to vary. Using a compactness method, we then derive H{\"o}lder regularity estimates for the gradient of the solutions.",

keywords = "Deforming kernels, Integro-differential equations, Monge-Amp{\`e}re equation, Nonlocal elliptic equations",

author = "{dos Prazeres}, Disson and Aelson Sobral and Urbano, {Jos{\'e} Miguel}",

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year = "2024",

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AU - dos Prazeres, Disson

AU - Sobral, Aelson

AU - Urbano, José Miguel

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Y1 - 2024/11/1

N2 - We derive Cordes-Nirenberg type results for nonlocal elliptic integro-differential equations with deforming kernels comparable to sections of a convex solution of a Monge-Ampère equation. Under a natural integrability assumption on the Monge-Ampère solution, we prove a stability lemma allowing the ellipticity class to vary. Using a compactness method, we then derive Hölder regularity estimates for the gradient of the solutions.

AB - We derive Cordes-Nirenberg type results for nonlocal elliptic integro-differential equations with deforming kernels comparable to sections of a convex solution of a Monge-Ampère equation. Under a natural integrability assumption on the Monge-Ampère solution, we prove a stability lemma allowing the ellipticity class to vary. Using a compactness method, we then derive Hölder regularity estimates for the gradient of the solutions.

KW - Deforming kernels

KW - Integro-differential equations

KW - Monge-Ampère equation

KW - Nonlocal elliptic equations

UR - http://www.scopus.com/inward/record.url?scp=85199764572&partnerID=8YFLogxK

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DO - 10.1016/j.jfa.2024.110593

M3 - Article

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VL - 287

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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M1 - 110593

ER -

Cordes-Nirenberg type results for nonlocal equations with deforming kernels

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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