Geometric Harmonic Analysis I : A Sharp Divergence Theorem with Nontangential Pointwise Traces

2022 ed.

by Dorina Mitrea , Irina Mitrea , Marius Mitrea

Book Details

Format Paperback / Softback

Book Series Developments in Mathematics

ISBN-10 3031059522

ISBN-13 9783031059520

Edition 2022 ed.

Publisher Springer International Publishing AG

Imprint Springer International Publishing AG

Country of Manufacture GB

Country of Publication GB

Publication Date Nov 6th, 2023

Print length 924 Pages

Product Classification: Complex analysis, complex variables Functional analysis & transforms

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This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.

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