Hodge Theory in the Sobolev Topology for the de Rham Complex, PDF eBook

Hodge Theory in the Sobolev Topology for the de Rham Complex PDF

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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

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