Description: Geometric Harmonic Analysis III by Dorina Mitrea, Irina Mitrea, Marius Mitrea 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 III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderón-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors. FORMAT Hardcover LANGUAGE English CONDITION Brand New Back Cover 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 III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calder Author Biography Table of Contents Introduction and Statement of Main Results Concerning the Divergence Theorem.- Examples, Counterexamples, and Additional Perspectives.- Tools from Geometric Measure Theory, Harmonic Analysis, and functional Analysis.- Open Sets with Locally Finite Surface Measures and Boundary Behavior.- Proofs of the Main Results Pertaining to the Divergence Theorem.- Applications to Singular Integrals, Function Spaces, Boundary Problems, and Further Results. Review "The complete set of volumes promises to deliver most of what is known about solving elliptic equations and systems on various kinds of flat domains under minimal conditions on the flatness (local and global) of the domains." (Raymond Johnson, zbMATH 1523.35001, 2023) Feature Presents a comprehensive novel theory for singular integral operators in optimal geometrical settings A great deal of applications are explored in detail The key results are new, with complete, essentially self-contained proofs Details ISBN3031227344 Author Marius Mitrea Short Title Geometric Harmonic Analysis III Publisher Springer International Publishing AG Series Developments in Mathematics Language English Year 2023 ISBN-10 3031227344 ISBN-13 9783031227349 Format Hardcover Series Number 74 DOI 10.1007/978-3-031-22735-6 Edition 1st Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Pages 972 Edition Description 1st ed. 2023 Publication Date 2023-05-13 Subtitle Integral Representations, Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering Alternative 9783031227370 DEWEY 515.4 Illustrations 1 Illustrations, color; 1 Illustrations, black and white; XVII, 972 p. 2 illus., 1 illus. in color. Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:142254058;
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Format: Hardcover
Language: English
ISBN-13: 9783031227349
Author: Dorina Mitrea, Irina Mitrea, Marius Mitrea
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Book Title: Geometric Harmonic Analysis III
