HODGE DECOMPOSITIONS WITH MIXED BOUNDARY CONDITIONS AND APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS ON LIPSCHITZ MANIFOLDS

摘要

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.