Regularity for anisotropic fully nonlinear integro-differential equations

Luis A. Caffarelli; Raimundo Leitão; José Miguel Urbano

doi:10.1007/s00208-014-1050-6

Regularity for anisotropic fully nonlinear integro-differential equations

Luis A. Caffarelli, Raimundo Leitão, José Miguel Urbano

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

12 Scopus citations

Abstract

We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We prove a nonlocal version of the ABP estimate, a Harnack inequality and the interior C 1,γ regularity, extending the results of Caffarelli and Silvestre (Comm Pure Appl Math 62:597–638, 2009) to the anisotropic case.

Original language	English (US)
Pages (from-to)	681-714
Number of pages	34
Journal	Mathematische Annalen
Volume	360
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-014-1050-6
State	Published - Dec 1 2014
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00208-014-1050-6

Cite this

@article{bef6f722080e4123960b1bfdc4a7fe27,

title = "Regularity for anisotropic fully nonlinear integro-differential equations",

abstract = "We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We prove a nonlocal version of the ABP estimate, a Harnack inequality and the interior C 1,γ regularity, extending the results of Caffarelli and Silvestre (Comm Pure Appl Math 62:597–638, 2009) to the anisotropic case.",

author = "Caffarelli, {Luis A.} and Raimundo Leit{\~a}o and Urbano, {Jos{\'e} Miguel}",

note = "Generated from Scopus record by KAUST IRTS on 2023-02-15",

year = "2014",

month = dec,

day = "1",

doi = "10.1007/s00208-014-1050-6",

language = "English (US)",

volume = "360",

pages = "681--714",

journal = "Mathematische Annalen",

issn = "1432-1807",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

T1 - Regularity for anisotropic fully nonlinear integro-differential equations

AU - Caffarelli, Luis A.

AU - Leitão, Raimundo

AU - Urbano, José Miguel

N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15

PY - 2014/12/1

Y1 - 2014/12/1

N2 - We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We prove a nonlocal version of the ABP estimate, a Harnack inequality and the interior C 1,γ regularity, extending the results of Caffarelli and Silvestre (Comm Pure Appl Math 62:597–638, 2009) to the anisotropic case.

AB - We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We prove a nonlocal version of the ABP estimate, a Harnack inequality and the interior C 1,γ regularity, extending the results of Caffarelli and Silvestre (Comm Pure Appl Math 62:597–638, 2009) to the anisotropic case.

UR - http://link.springer.com/10.1007/s00208-014-1050-6

UR - http://www.scopus.com/inward/record.url?scp=84939893568&partnerID=8YFLogxK

U2 - 10.1007/s00208-014-1050-6

DO - 10.1007/s00208-014-1050-6

M3 - Article

SN - 1432-1807

VL - 360

SP - 681

EP - 714

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

Regularity for anisotropic fully nonlinear integro-differential equations

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this