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

by G. S. Alberti

(Report number 2016-22)

Abstract
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.

Keywords: Maxwell's equations, Hölder regularity, optimal regularity, Schauder estimates, anisotropic media, bianisotropic media, Helmholtz decomposition.

@Techreport{A16_659,
  author = {G. S. Alberti},
  title = {H\"older regularity for Maxwell's equations under minimal assumptions on the coefficients},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-22},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-22.pdf },
  year = {2016}
}

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