Green’s function for second order elliptic equations with singular lower order coefficients

Seick Kim; Georgios Sakellaris

doi:10.1080/03605302.2018.1543318

Green’s function for second order elliptic equations with singular lower order coefficients

Seick Kim, Georgios Sakellaris

Department of Mathematics

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

19 Citations (Scopus)

Abstract

We construct Green’s function for second order elliptic operators of the form (Formula presented.) in a domain and obtain pointwise bounds, as well as Lorentz space bounds. We assume that the matrix of principal coefficients (Formula presented.) is uniformly elliptic and bounded and the lower order coefficients b, c, and d belong to certain Lebesgue classes and satisfy the condition (Formula presented.). In particular, we allow the lower order coefficients to be singular. We also obtain the global pointwise bounds for the gradient of Green’s function in the case when the mean oscillations of the coefficients (Formula presented.) and b satisfy the Dini conditions and the domain is (Formula presented.).

Original language	English
Pages (from-to)	228-270
Number of pages	43
Journal	Communications in Partial Differential Equations
Volume	44
Issue number	3
DOIs	https://doi.org/10.1080/03605302.2018.1543318
Publication status	Published - 2019 Mar 4

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Taylor & Francis Group, LLC.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1080/03605302.2018.1543318

Cite this

@article{51c7ec9fcdc74436a7b66fc8c8a7d00b,

title = "Green{\textquoteright}s function for second order elliptic equations with singular lower order coefficients",

abstract = "We construct Green{\textquoteright}s function for second order elliptic operators of the form (Formula presented.) in a domain and obtain pointwise bounds, as well as Lorentz space bounds. We assume that the matrix of principal coefficients (Formula presented.) is uniformly elliptic and bounded and the lower order coefficients b, c, and d belong to certain Lebesgue classes and satisfy the condition (Formula presented.). In particular, we allow the lower order coefficients to be singular. We also obtain the global pointwise bounds for the gradient of Green{\textquoteright}s function in the case when the mean oscillations of the coefficients (Formula presented.) and b satisfy the Dini conditions and the domain is (Formula presented.).",

keywords = "Dini mean oscillation, Green{\textquoteright}s function, Lorentz bounds, pointwise bounds, singular lower order coefficients",

author = "Seick Kim and Georgios Sakellaris",

note = "Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Taylor & Francis Group, LLC.",

year = "2019",

month = mar,

day = "4",

doi = "10.1080/03605302.2018.1543318",

language = "English",

volume = "44",

pages = "228--270",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "3",

}

TY - JOUR

T1 - Green’s function for second order elliptic equations with singular lower order coefficients

AU - Kim, Seick

AU - Sakellaris, Georgios

PY - 2019/3/4

Y1 - 2019/3/4

N2 - We construct Green’s function for second order elliptic operators of the form (Formula presented.) in a domain and obtain pointwise bounds, as well as Lorentz space bounds. We assume that the matrix of principal coefficients (Formula presented.) is uniformly elliptic and bounded and the lower order coefficients b, c, and d belong to certain Lebesgue classes and satisfy the condition (Formula presented.). In particular, we allow the lower order coefficients to be singular. We also obtain the global pointwise bounds for the gradient of Green’s function in the case when the mean oscillations of the coefficients (Formula presented.) and b satisfy the Dini conditions and the domain is (Formula presented.).

AB - We construct Green’s function for second order elliptic operators of the form (Formula presented.) in a domain and obtain pointwise bounds, as well as Lorentz space bounds. We assume that the matrix of principal coefficients (Formula presented.) is uniformly elliptic and bounded and the lower order coefficients b, c, and d belong to certain Lebesgue classes and satisfy the condition (Formula presented.). In particular, we allow the lower order coefficients to be singular. We also obtain the global pointwise bounds for the gradient of Green’s function in the case when the mean oscillations of the coefficients (Formula presented.) and b satisfy the Dini conditions and the domain is (Formula presented.).

KW - Dini mean oscillation

KW - Green’s function

KW - Lorentz bounds

KW - pointwise bounds

KW - singular lower order coefficients

UR - http://www.scopus.com/inward/record.url?scp=85059452495&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059452495&partnerID=8YFLogxK

U2 - 10.1080/03605302.2018.1543318

DO - 10.1080/03605302.2018.1543318

M3 - Article

AN - SCOPUS:85059452495

SN - 0360-5302

VL - 44

SP - 228

EP - 270

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 3

ER -

Green’s function for second order elliptic equations with singular lower order coefficients

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this