Dorina Mitrea, Irina Mitrea, Marius Mitrea

Geometric Harmonic Analysis III (eBook, PDF)

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

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 972
• Erscheinungstermin: 12. Mai 2023
• Englisch
• ISBN-13: 9783031227356
• Artikelnr.: 68028740

Inhaltsangabe

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.

Rezensionen

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)