03285nam 22005175 450 991074118650332120251113175920.03-031-31561-810.1007/978-3-031-31561-9(CKB)28013438300041(MiAaPQ)EBC30718776(Au-PeEL)EBL30718776(DE-He213)978-3-031-31561-9(PPN)272260606(EXLCZ)992801343830004120230822d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGeometric Harmonic Analysis V Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems /by Dorina Mitrea, Irina Mitrea, Marius Mitrea1st ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (1006 pages)Developments in Mathematics,2197-795X ;769783031315602 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.The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.Developments in Mathematics,2197-795X ;76Mathematical analysisIntegral Transforms and Operational CalculusMathematical analysis.Integral Transforms and Operational Calculus.515.42Mitrea Dorina1965-1171699Mitrea IrinaMitrea MariusMiAaPQMiAaPQMiAaPQBOOK9910741186503321Geometric harmonic analysis V3555317UNINA