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arXiv · 1307.0350

Elliptic regularity theory applied to time harmonic anisotropic Maxwell's equations with less than Lipschitz complex coefficients

Giovanni S. Alberti·Yves Capdeboscq
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Abstract

The focus of this paper is the study of the regularity properties of the time harmonic Maxwell's equations with anisotropic complex coefficients, in a bounded domain with $C^{1,1}$ boundary. We assume that at least one of the material parameters is $W^{1,3+\delta}$ for some $\delta>0$. Using regularity theory for second order elliptic partial differential equations, we derive $W^{1,p}$ estimates and H\"older estimates for electric and magnetic fields up to the boundary. We also derive interior estimates in bi-anisotropic media.

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Giovanni S. Alberti, Yves Capdeboscq. 2013-07-01. Elliptic regularity theory applied to time harmonic anisotropic Maxwell's equations with less than Lipschitz complex coefficients. https://doi.org/10.1137/130929539

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