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

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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 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.

Original languageEnglish
Pages (from-to)87-100
Number of pages14
JournalSIAM Journal on Mathematical Analysis
Volume34
Issue number1
DOIs
Publication statusPublished - 2003

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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