Elliptic systems with measurable coefficients of the type of Lamé system in three dimensions

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study the 3×3 elliptic systems ∇(a(x)∇×u)-∇(b(x)∇·u)=f, where the coefficients a(x) and b(x) are positive scalar functions that are measurable and bounded away from zero and infinity. We prove that weak solutions of the above system are Hölder continuous under some minimal conditions on the inhomogeneous term f. We also present some applications and discuss several related topics including estimates of the Green's functions and the heat kernels of the above systems.

Original languageEnglish
Pages (from-to)2466-2493
Number of pages28
JournalJournal of Differential Equations
Volume251
Issue number9
DOIs
Publication statusPublished - 2011 Nov 1

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Elliptic Systems
Green's function
Three-dimension
Heat Kernel
Coefficient
Weak Solution
Infinity
Scalar
Zero
Term
Estimate
Hot Temperature

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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title = "Elliptic systems with measurable coefficients of the type of Lam{\'e} system in three dimensions",
abstract = "We study the 3×3 elliptic systems ∇(a(x)∇×u)-∇(b(x)∇·u)=f, where the coefficients a(x) and b(x) are positive scalar functions that are measurable and bounded away from zero and infinity. We prove that weak solutions of the above system are H{\"o}lder continuous under some minimal conditions on the inhomogeneous term f. We also present some applications and discuss several related topics including estimates of the Green's functions and the heat kernels of the above systems.",
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Elliptic systems with measurable coefficients of the type of Lamé system in three dimensions. / Kang, Kyungkeun; Kim, Seick.

In: Journal of Differential Equations, Vol. 251, No. 9, 01.11.2011, p. 2466-2493.

Research output: Contribution to journalArticle

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AU - Kang, Kyungkeun

AU - Kim, Seick

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N2 - We study the 3×3 elliptic systems ∇(a(x)∇×u)-∇(b(x)∇·u)=f, where the coefficients a(x) and b(x) are positive scalar functions that are measurable and bounded away from zero and infinity. We prove that weak solutions of the above system are Hölder continuous under some minimal conditions on the inhomogeneous term f. We also present some applications and discuss several related topics including estimates of the Green's functions and the heat kernels of the above systems.

AB - We study the 3×3 elliptic systems ∇(a(x)∇×u)-∇(b(x)∇·u)=f, where the coefficients a(x) and b(x) are positive scalar functions that are measurable and bounded away from zero and infinity. We prove that weak solutions of the above system are Hölder continuous under some minimal conditions on the inhomogeneous term f. We also present some applications and discuss several related topics including estimates of the Green's functions and the heat kernels of the above systems.

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