Hodge Theory in the Sobolev Topology for the de Rham Complex
Author： Luigi Fontana;Steven G. Krantz;Marco M. Peloso
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470402112
P-ISBN(Paperback): 9780821808306
P-ISBN(Hardback): 9780821808306
Subject： O175.2 Partial Differential Equations
Keyword： Analysis
Language： ENG
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Hodge Theory in the Sobolev Topology for the de Rham Complex
Description
In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L^2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. Features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems theorems completely explained and proved new geometric tools for differential analysis on domains and manifolds