Geometric Harmonic Analysis I (eBook)

A Sharp Divergence Theorem with Nontangential Pointwise Traces

Dorina Mitrea, Irina Mitrea, Marius Mitrea (Autoren)

eBook Download: PDF

2022 | 1st ed. 2022
XXVIII, 924 Seiten
Springer International Publishing (Verlag)
978-3-031-05950-6 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 4.11.2022
• Reihe/Serie: Developments in Mathematics
• Reihe/Serie: Developments in Mathematics
• Zusatzinfo: XXVIII, 924 p. 44 illus., 20 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: Ahlfors regular domain • bounded mean oscillations • Clifford Algebras • differential forms • Divergence Theorem • First-Order System • Gauss-Green theorem • Hardy-Littlewood maximal function • Integration by parts • nontangentially accessible boundary • nontangential maximal function • NTA domain • quasi-metric spaces • regular SKT domain • Reifenberg flat domain • Riemannian manifold • spaces of homogenous type • Stokes Theorem • uniform domain • vanishing mean oscillations
• ISBN-10: 3-031-05950-6 / 3031059506
• ISBN-13: 978-3-031-05950-6 / 9783031059506