Elliptic systems with measurable coefficients of the type of Lamé system in three dimensions |
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Authors: | Kyungkeun Kang |
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Affiliation: | Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea |
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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. |
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Keywords: | primary, 35J47, 35B45 secondary, 35J57 |
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