An H^s,p(\curl;Ω) estimate for the Maxwell system

2014/08/10 by Manas Kar, Kar, Manas, Mourad Sini +1
Computer Science · Mathematics · Engineering · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.1408.2203

Abstract

We derive an H₀^s,p(\curl;Ω) estimate for the solutions of the Maxwell type equations modeled with anisotropic and W^{s, ∞}(Ω)-regular coefficients. Here, we obtain the regularity of the solutions for the integrability and smoothness indices (p, s) in a plan domain characterized by the apriori lower/upper bounds of a and the apriori upper bound of its Hölder semi-norm of order s. The proof relies on a perturbation argument generalizing Gröger's L^p-type estimate, known for the elliptic problems, to the Maxwell system.

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