Geometric Harmonic Analysis I
| Autor: | Dorina Mitrea, Irina Mitrea, Marius Mitrea |
|---|---|
| EAN: | 9783031059506 |
| eBook Format: | |
| Sprache: | Englisch |
| Produktart: | eBook |
| Veröffentlichungsdatum: | 04.11.2022 |
| Untertitel: | A Sharp Divergence Theorem with Nontangential Pointwise Traces |
| Kategorie: | |
| Schlagworte: | Divergence theorem;Gauss-Green theorem;Stokes theorem;nontangential maximal function;nontangentially accessible boundary;Ahlfors regular domain;NTA domain;uniform domain;Reifenberg flat domain;regular SKT domain;Riemannian manifold;differential forms |
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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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