Geometric Harmonic Analysis III: Integral Representations, Calderón-Zygmund Theory, Fatou Theorems, and...

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Dorina Mitrea Irina Mitrea

Geometric Harmonic Analysis III

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

Dorina Mitrea, Irina Mitrea, Marius Mitrea

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English

Springer International Publishing AG
13 May 2023

Integral calculus & equations

Series: Developments in Mathematics

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.

By: Dorina Mitrea, Irina Mitrea, Marius Mitrea
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2023 ed.
Volume: 74
Dimensions: Height: 235mm, Width: 155mm,
Weight: 1.646kg
ISBN: 9783031227349
ISBN 10: 3031227344
Series: Developments in Mathematics
Pages: 972
Publication Date: 13 May 2023
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Geometric Harmonic Analysis III: Integral Representations, Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering

“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)