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

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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

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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