03499nam 22005655 450 991072508800332120240117155812.09783031227356(electronic bk.)978303122734910.1007/978-3-031-22735-6(MiAaPQ)EBC7248830(Au-PeEL)EBL7248830(DE-He213)978-3-031-22735-6(BIP)086286147(PPN)270612653(EXLCZ)992663787990004120230512d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGeometric Harmonic Analysis III[electronic resource] Integral Representations, Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering /by Dorina Mitrea, Irina Mitrea, Marius Mitrea1st ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (980 pages)Developments in Mathematics,2197-795X ;74Print version: Mitrea, Dorina Geometric Harmonic Analysis III Cham : Springer International Publishing AG,c2023 9783031227349 Includes bibliographical references.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.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.Developments in Mathematics,2197-795X ;74Mathematical analysisIntegral Transforms and Operational CalculusTeoria de la mesura geomètricathubLlibres electrònicsthubMathematicsMathematical analysis.Integral Transforms and Operational Calculus.Teoria de la mesura geomètrica515.4Mitrea Dorina1965-1171699Mitrea IrinaMitrea MariusMiAaPQMiAaPQMiAaPQ9910725088003321Geometric Harmonic Analysis III3566859UNINA