Hodge decompositions with mixed boundary conditions and applications to partial differential equations on lipschitz manifolds

Abstract

We study boundary-value problems with mixed boundary conditions in weakly Lipschitz domains of compact boundaryless Riemannian Lipschitz manifolds. These include the case of the Maxwell system, the Hodge–Dirac operator, and the Hodge–Laplacian. Our approach brings to bear tools from functional analysis, differential geometry, harmonic analysis, and topology. Bibliography: 45 titles.