A note on local higher regularity in the dynamic linear relaxed micromorphic model. (26th July 2021)

• Record Type: Journal Article
• Authors: Owczarek, Sebastian; Ghiba, Ionel‐Dumitrel; Neff, Patrizio
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 18(2022)
• Page Start: 13855
• Page End: 13865
• Publication Date: 2021-07-26
• Subjects: extension operator -- generalized continua -- local regularity -- tangential trace; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7661
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We consider the regularity question of solutions for the dynamic initial‐boundary value problem for the linear relaxed micromorphic model. This generalized continuum model couples a wave‐type equation for the displacement with a generalized Maxwell‐type wave equation for the microdistortion. Naturally, solutions are found in H 1 for the displacement u and H(Curl) for the microdistortion P . Using energy estimates for difference quotients, we improve this regularity. We show H loc 1 –regularity for the displacement field, H loc 1 –regularity for the microdistortion tensor P and that Curl P is H 1 –regular if the data are sufficiently smooth.