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Bibliographic Details
Main Authors: Knees, Dorothee, Owczarek, Sebastian, Neff, Patrizio
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2403.17451
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Table of Contents:
  • In this paper, we investigate the global higher regularity properties of weak solutions for a linear elliptic system coupled with a nonlinear Maxwell-type system defined on Lipschitz domains. The regularity result is established using a modified finite difference approach. These adjusted finite differences involve inner variations in conjunction with a Piola-type transformation to preserve the curl-structure within the matrix Maxwell system. The proposed method is further applied to the linear relaxed micromorphic model. As a result, for a physically nonlinear version of the relaxed micromorphic model, we demonstrate that for arbitrary $ε> 0$, the displacement vector $u$ belongs to $H^{\frac{3}{2}-ε}(Ω)$, and the microdistortion tensor $P$ belongs to $H^{\frac{1}{2}-ε}(Ω)$ while $\Curl P$ belongs to $H^{\frac{1}{2}-ε}(Ω)$.