A Hölder Regularity Theory for a Class of Non-Local Elliptic Equations Related to Subordinate Brownian Motions

Ildoo Kim; Kyeong Hun Kim

doi:10.1007/s11118-015-9490-5

A Hölder Regularity Theory for a Class of Non-Local Elliptic Equations Related to Subordinate Brownian Motions

Ildoo Kim, Kyeong Hun Kim

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

6 Citations (Scopus)

Abstract

In this article we present the existence, uniqueness, and Hölder regularity of solutions for the non-local elliptic equations of the type (Formula presented.) where (Formula presented.) Here χ(y) is a suitable indicator function, J(y)dy is a rotationally invariant Lévy measure on ℝ^d (Formula presented.), and a(y) is an only measurable function with positive lower and upper bounds.

Original language	English
Pages (from-to)	653-673
Number of pages	21
Journal	Potential Analysis
Volume	43
Issue number	4
DOIs	https://doi.org/10.1007/s11118-015-9490-5
Publication status	Published - 2015 Nov 1

Bibliographical note

Funding Information:
This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1401-02.

Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.

Keywords

Hölder estimates
Integro-differential equations
Non-local elliptic equations
Non-symmetric measurable kernels
Subordinate Brownian motion

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s11118-015-9490-5

Cite this

@article{d8ef56089dd248468360338dfe7d8bd9,

title = "A H{\"o}lder Regularity Theory for a Class of Non-Local Elliptic Equations Related to Subordinate Brownian Motions",

abstract = "In this article we present the existence, uniqueness, and H{\"o}lder regularity of solutions for the non-local elliptic equations of the type (Formula presented.) where (Formula presented.) Here χ(y) is a suitable indicator function, J(y)dy is a rotationally invariant L{\'e}vy measure on ℝd (Formula presented.), and a(y) is an only measurable function with positive lower and upper bounds.",

keywords = "H{\"o}lder estimates, Integro-differential equations, Non-local elliptic equations, Non-symmetric measurable kernels, Subordinate Brownian motion",

author = "Ildoo Kim and Kim, {Kyeong Hun}",

note = "Funding Information: This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1401-02. Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media Dordrecht.",

year = "2015",

month = nov,

day = "1",

doi = "10.1007/s11118-015-9490-5",

language = "English",

volume = "43",

pages = "653--673",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - A Hölder Regularity Theory for a Class of Non-Local Elliptic Equations Related to Subordinate Brownian Motions

AU - Kim, Ildoo

AU - Kim, Kyeong Hun

N1 - Funding Information: This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1401-02. Publisher Copyright: © 2015, Springer Science+Business Media Dordrecht.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - In this article we present the existence, uniqueness, and Hölder regularity of solutions for the non-local elliptic equations of the type (Formula presented.) where (Formula presented.) Here χ(y) is a suitable indicator function, J(y)dy is a rotationally invariant Lévy measure on ℝd (Formula presented.), and a(y) is an only measurable function with positive lower and upper bounds.

AB - In this article we present the existence, uniqueness, and Hölder regularity of solutions for the non-local elliptic equations of the type (Formula presented.) where (Formula presented.) Here χ(y) is a suitable indicator function, J(y)dy is a rotationally invariant Lévy measure on ℝd (Formula presented.), and a(y) is an only measurable function with positive lower and upper bounds.

KW - Hölder estimates

KW - Integro-differential equations

KW - Non-local elliptic equations

KW - Non-symmetric measurable kernels

KW - Subordinate Brownian motion

UR - http://www.scopus.com/inward/record.url?scp=84949208183&partnerID=8YFLogxK

U2 - 10.1007/s11118-015-9490-5

DO - 10.1007/s11118-015-9490-5

M3 - Article

AN - SCOPUS:84949208183

SN - 0926-2601

VL - 43

SP - 653

EP - 673

JO - Potential Analysis

JF - Potential Analysis

IS - 4

ER -

A Hölder Regularity Theory for a Class of Non-Local Elliptic Equations Related to Subordinate Brownian Motions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this