Geometric Harmonic Analysis III

Integral Representations, Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering

AvDorina Mitrea,Irina Mitrea

Inbunden, Engelska, 2023

Del i serien Developments in Mathematics

2 121 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2023-05-13
Mått:155 x 235 x 59 mm
Vikt:1 630 g
Format:Inbunden
Språk:Engelska
Serie:Developments in Mathematics
Antal sidor:972
Upplaga:2023
Förlag:Springer International Publishing AG
ISBN:9783031227349

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

“The book is really well written. Each chapter and every section contains discursive paragraphs where the authors introduce the reader to the general content of the text and guide them through the path of the following theorems and proofs. ... For sure, this book contains a wealth of mathematical ideas which are worth being explored by working mathematicians.” (Marco Bramanti, Mathematical Reviews, June, 2025) “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)

Innehållsförteckning

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.