On the hölder continuity of solutions of a certain system related to Maxwell's equations

Kyungkeun Kang; Seick Kim

doi:10.1137/S0036141001393341

On the hölder continuity of solutions of a certain system related to Maxwell's equations

Kyungkeun Kang, Seick Kim

Department of Mathematics

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

17 Citations (Scopus)

Abstract

We study the system curl (a(x) curl u) = 0, div u = 0 with a bounded measurable coefficient a(x). The main result of this paper is the Hölder continuity of weak solutions of the system above. As an application, we prove the C^α regularity of weak solutions of the Maxwell's equations in a quasi-stationary electromagnetic field.

Original language	English
Pages (from-to)	87-100
Number of pages	14
Journal	SIAM Journal on Mathematical Analysis
Volume	34
Issue number	1
DOIs	https://doi.org/10.1137/S0036141001393341
Publication status	Published - 2003

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/S0036141001393341

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abstract = "We study the system curl (a(x) curl u) = 0, div u = 0 with a bounded measurable coefficient a(x). The main result of this paper is the H{\"o}lder continuity of weak solutions of the system above. As an application, we prove the Cα regularity of weak solutions of the Maxwell's equations in a quasi-stationary electromagnetic field.",

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AU - Kim, Seick

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N2 - We study the system curl (a(x) curl u) = 0, div u = 0 with a bounded measurable coefficient a(x). The main result of this paper is the Hölder continuity of weak solutions of the system above. As an application, we prove the Cα regularity of weak solutions of the Maxwell's equations in a quasi-stationary electromagnetic field.

AB - We study the system curl (a(x) curl u) = 0, div u = 0 with a bounded measurable coefficient a(x). The main result of this paper is the Hölder continuity of weak solutions of the system above. As an application, we prove the Cα regularity of weak solutions of the Maxwell's equations in a quasi-stationary electromagnetic field.

KW - Interior regularity

KW - Maxwell's equations

KW - Measurable coefficients

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JO - SIAM Journal on Mathematical Analysis

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ER -

On the hölder continuity of solutions of a certain system related to Maxwell's equations

Abstract

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