Green's functions for elliptic and parabolic systems with Robin-type boundary conditions

Jongkeun Choi, Seick Kim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The aim of this paper is to investigate Green's function for parabolic and elliptic systems satisfying a possibly nonlocal Robin-type boundary condition. We construct Green's function for parabolic systems with time-dependent coefficients satisfying a possibly nonlocal Robin-type boundary condition assuming that weak solutions of the system are locally Hölder continuous in the interior of the domain, and as a corollary we construct Green's function for elliptic system with a Robin-type condition. Also, we obtain Gaussian bound for Robin Green's function under an additional assumption that weak solutions of Robin problem are locally bounded up to the boundary. We provide some examples satisfying such a local boundedness property, and thus have Gaussian bounds for their Green's functions.

Original languageEnglish
Pages (from-to)3205-3261
Number of pages57
JournalJournal of Functional Analysis
Volume267
Issue number9
DOIs
Publication statusPublished - 2014 Nov 1

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Parabolic Systems
Elliptic Systems
Green's function
Boundary conditions
Weak Solution
Robin Problem
Boundedness
Corollary
Interior
Coefficient

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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abstract = "The aim of this paper is to investigate Green's function for parabolic and elliptic systems satisfying a possibly nonlocal Robin-type boundary condition. We construct Green's function for parabolic systems with time-dependent coefficients satisfying a possibly nonlocal Robin-type boundary condition assuming that weak solutions of the system are locally H{\"o}lder continuous in the interior of the domain, and as a corollary we construct Green's function for elliptic system with a Robin-type condition. Also, we obtain Gaussian bound for Robin Green's function under an additional assumption that weak solutions of Robin problem are locally bounded up to the boundary. We provide some examples satisfying such a local boundedness property, and thus have Gaussian bounds for their Green's functions.",
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Green's functions for elliptic and parabolic systems with Robin-type boundary conditions. / Choi, Jongkeun; Kim, Seick.

In: Journal of Functional Analysis, Vol. 267, No. 9, 01.11.2014, p. 3205-3261.

Research output: Contribution to journalArticle

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