Fully nonlinear integro-differential equations with deforming kernels

Luis Caffarelli; Rafayel Teymurazyan; José Miguel Urbano

doi:10.1080/03605302.2020.1739706

Fully nonlinear integro-differential equations with deforming kernels

Luis Caffarelli, Rafayel Teymurazyan, José Miguel Urbano

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

7 Scopus citations

Abstract

We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge–Ampère equation. We prove an ABP estimate and a Harnack inequality, and derive Hölder and (Formula presented.) regularity results for solutions.

Original language	English (US)
Pages (from-to)	847-871
Number of pages	25
Journal	Communications in Partial Differential Equations
Volume	45
Issue number	8
DOIs	https://doi.org/10.1080/03605302.2020.1739706
State	Published - Aug 2 2020
Externally published	Yes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2020.1739706

Cite this

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abstract = "We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge–Amp{\`e}re equation. We prove an ABP estimate and a Harnack inequality, and derive H{\"o}lder and (Formula presented.) regularity results for solutions.",

author = "Luis Caffarelli and Rafayel Teymurazyan and Urbano, {Jos{\'e} Miguel}",

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AU - Caffarelli, Luis

AU - Teymurazyan, Rafayel

AU - Urbano, José Miguel

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PY - 2020/8/2

Y1 - 2020/8/2

N2 - We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge–Ampère equation. We prove an ABP estimate and a Harnack inequality, and derive Hölder and (Formula presented.) regularity results for solutions.

AB - We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge–Ampère equation. We prove an ABP estimate and a Harnack inequality, and derive Hölder and (Formula presented.) regularity results for solutions.

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UR - http://www.scopus.com/inward/record.url?scp=85081745924&partnerID=8YFLogxK

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DO - 10.1080/03605302.2020.1739706

M3 - Article

SN - 1532-4133

VL - 45

SP - 847

EP - 871

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 8

ER -

Fully nonlinear integro-differential equations with deforming kernels

Abstract

Bibliographical note

ASJC Scopus subject areas

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