A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains and a Corresponding Generalized $\mathrm{A}_{0}^{*}$-$\mathrm{A}_{1}$-Lemma in Hilbert Spaces

Autor:	Pauly, Dirk
Rok vydání:	2017
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics Mathematics - Functional Analysis 35B27 35Q61 47B07 46B50
Druh dokumentu:	Working Paper
Popis:	We prove global and local versions of the so-called div-curl-lemma, a crucial result in the homogenization theory of partial differential equations, for mixed boundary conditions on bounded weak Lipschitz domains in 3D with weak Lipschitz interfaces. We will generalize our results using an abstract Hilbert space setting, which shows corresponding results to hold in arbitrary dimensions as well as for various differential operators. The crucial tools and the core of our arguments are Hilbert complexes and related compact embeddings. Comment: key words: div-curl-lemma, compensated compactness, mixed boundary conditions, weak Lipschitz domains, Maxwell's equations
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1707.00019 Zobrazit plný text záznamu View this record from Arxiv