Hodge theory in the Sobolev topology for the de Rham complex

1996/01/22 by Luigi Fontana, Fontana, Luigi, Steven G. Krantz +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.math/9601208

arxiv created 1996/01/22 · arxiv updated 2016/09/06

Abstract

The authors study the Hodge theory of the exterior differential operator d acting on q-forms on a smoothly bounded domain in \RR^N+1, and on the half space \rnp. The novelty is that the topology used is not an L² topology but a Sobolev topology. This strikingly alters the problem as compared to the classical setup. It gives rise to a boundary-value problem belonging to a class of problems first introduced by Višik and Eskin, and by Boutet de Monvel.

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