Abstract
Abstract
We prove global and local versions of the so-called
{\operatorname{div}}
-
{\operatorname{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.
Subject
Applied Mathematics,Numerical Analysis,Analysis
Reference80 articles.
1. On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma;Trends in Applications of Mathematics to Mechanics,2018
2. Compacité par compensation;Ann. Sc. Norm. Super. Pisa Cl. Sci. (4),1978
3. On the boundary value problems of electro- and magnetostatics;Proc. Roy. Soc. Edinburgh Sect. A,1982
4. Maxwell’s boundary value problem on Riemannian manifolds with nonsmooth boundaries;J. Math. Anal. Appl.,1974
5. A remark on the regularity of solutions of Maxwell’s equations on Lipschitz domains;Math. Methods Appl. Sci.,1990
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