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

Kyungkeun Kang; Seick Kim

doi:10.1016/j.jde.2011.07.015

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

Kyungkeun Kang, Seick Kim

Department of Mathematics

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

6 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 language	English
Pages (from-to)	2466-2493
Number of pages	28
Journal	Journal of Differential Equations
Volume	251
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2011.07.015
Publication status	Published - 2011 Nov 1

Bibliographical note

Funding Information:
This work was supported by WCU (World Class University) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (R31-2008-000-10049-0). Kyungkeun Kang was supported by the Korean Research Foundation Grant (MOEHRD, Basic Research Promotion Fund, KRF-2008-331-C00024) and the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0088692). Seick Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0008224).

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2011.07.015

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.",

author = "Kyungkeun Kang and Seick Kim",

note = "Funding Information: This work was supported by WCU (World Class University) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (R31-2008-000-10049-0). Kyungkeun Kang was supported by the Korean Research Foundation Grant (MOEHRD, Basic Research Promotion Fund, KRF-2008-331-C00024) and the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0088692). Seick Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0008224).",

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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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ER -

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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