Hölder regularity for Maxwell’s equations under minimal assumptions on the coefficients

We prove global Hölder regularity for the solutions to the time-harmonic anisotropic Maxwell’s equations, under the assumptions of Hölder continuous coefficients. The regularity hypotheses on the coefficients are minimal. The same estimates hold also in the case of bianisotropic material parameters....

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 57; no. 3; pp. 1 - 11
Main Author Alberti, Giovanni S.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Springer Nature B.V
Subjects
Analysis
Calculus of Variations and Optimal Control; Optimization
Coefficients
Control
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Maxwell's equations
Regularity
Systems Theory
Theoretical
35B65
35Q61
35J57
35Q60
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Summary:We prove global Hölder regularity for the solutions to the time-harmonic anisotropic Maxwell’s equations, under the assumptions of Hölder continuous coefficients. The regularity hypotheses on the coefficients are minimal. The same estimates hold also in the case of bianisotropic material parameters.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-018-1358-2