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001451231 020__ $$a9783031059506$$q(electronic bk.)
001451231 020__ $$a3031059506$$q(electronic bk.)
001451231 020__ $$z9783031059490
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001451231 0247_ $$a10.1007/978-3-031-05950-6$$2doi
001451231 035__ $$aSP(OCoLC)1350842494
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001451231 1001_ $$aMitrea, Dorina,$$d1965-$$eauthor.$$1https://isni.org/isni/0000000110350758
001451231 24510 $$aGeometric harmonic analysis.$$nI,$$pA sharp divergence theorem with nontangential pointwise traces /$$cDorina Mitrea, Irina Mitrea, Marius Mitrea.
001451231 24630 $$aSharp divergence theorem with nontangential pointwise traces
001451231 264_1 $$aCham :$$bSpringer,$$c2022.
001451231 300__ $$a1 online resource :$$billustrations (black and white, and color).
001451231 336__ $$atext$$btxt$$2rdacontent
001451231 337__ $$acomputer$$bc$$2rdamedia
001451231 338__ $$aonline resource$$bcr$$2rdacarrier
001451231 4901_ $$aDevelopments in mathematics ;$$vvolume 72
001451231 504__ $$aIncludes bibliographical references and indexes.
001451231 5050_ $$aPrefacing this Series -- Statement of Main Results Concerning the Divergence Theorem -- Examples, Counterexamples, and Additional Perspectives -- Measure Theoretical and Topological Rudiments -- Sets of Locally Finite Perimeter and Other Categories of Euclidean Sets -- Tools from Harmonic Analysis -- Quasi-Metric Spaces and Spaces of Homogenous Type -- Open Sets with Locally Finite Surface Measures and Boundary Behavior -- Proofs of Main Results Pertaining to the Divergence Theorem -- II: Function Spaces Measuring Size and Smoothness on Rough Sets -- Preliminary Functional Analytic Matters -- Selected Topics in Distribution Theory -- Hardy Spaces on Ahlfors Regular Sets -- Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets -- Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets -- Boundary Traces from Weighted Sobolev Spaces in Besov Spaces -- Besov and Triebel-Lizorkin Spaces in Open Sets -- Strong and Weak Normal Boundary Traces of Vector Fields in Hardy and Morney Spaces -- Sobolev Spaces on the Geometric Measure Theoretic boundary of Sets of Locally Finite Perimeter -- III: Integral Representations Calderon-Zygmund Theory, Fatou Theorems, and Applications to Scattering -- Integral Representations and Integral Identities -- Calderon-Zygmund Theory on Uniformly Rectifiable Sets -- Quantitative Fatou-Type Theorems in Arbitrary UR Domains -- Scattering by Rough Obstacles -- IV: Boundary Layer Potentials on Uniformly Rectifiable Domains, and Applications to Complex Analysis -- Layer Potential Operators on Lebesgue and Sobolev Spaces -- Layer Potential Operators on Hardy, BMO, VMO, and Holder Spaces -- Layer Potential Operators on Calderon, Morrey-Campanato, and Morrey Spaces -- Layer Potential Operators Acting from Boundary Besov and Triebel-Lizorkin Spaces -- Generalized double Layers in Uniformly Rectifiable Domains -- Green Formulas and Layer Potential Operators for the Stokes System -- Applications to Analysis in Several Complex Variables -- V: Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems -- Abstract Fredholm Theory -- Distinguished Coefficient Tensors -- Failure of Fredholm Solvability for Weakly Elliptic Systems -- Quantifying Global and Infinitesimal Flatness -- Norm Estimates and Invertibility Results for SIO's on Unbounded Boundaries -- Estimating Chord-Dot-Normal SIO's on Domains with Compact Boundaries -- The Radon-Carleman Problem -- Fredholmness and Invertibility of Layer Potentials on Compact Boundaries -- Green Functions and Uniqueness for Boundary Problems for Second-Order Systems -- Green Functions and Poisson Kernels for the Laplacian -- Boundary Value Problems for Elliptic Systems in Rough Domains.
001451231 506__ $$aAccess limited to authorized users.
001451231 520__ $$aThis monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.
001451231 588__ $$aDescription based on print version record.
001451231 650_0 $$aDivergence theorem.
001451231 655_0 $$aElectronic books.
001451231 7001_ $$aMitrea, Irina,$$eauthor.$$1https://isni.org/isni/0000000403626797
001451231 7001_ $$aMitrea, Marius,$$eauthor.$$1https://isni.org/isni/0000000116450995
001451231 77608 $$iPrint version:$$aMitrea, Dorina, 1965-$$tGeometric harmonic analysis. I, A sharp divergence theorem with nontangential pointwise traces.$$dCham : Springer, 2022$$z9783031059490$$w(OCoLC)1338682180
001451231 830_0 $$aDevelopments in mathematics ;$$vv. 72.
001451231 852__ $$bebk
001451231 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-05950-6$$zOnline Access$$91397441.1
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