Geometric harmonic analysis.. I,. A ...
Mitrea, Dorina.

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  • Geometric harmonic analysis.. I,. A sharp divergence theorem with nontangential pointwise traces
  • 紀錄類型: 書目-電子資源 : Monograph/item
    正題名/作者: Geometric harmonic analysis./ by Dorina Mitrea, Irina Mitrea, Marius Mitrea.
    其他題名: Sharp divergence theorem with nontangential pointwise traces
    作者: Mitrea, Dorina.
    其他作者: Mitrea, Irina.
    出版者: Cham :Springer International Publishing : : 2022.,
    面頁冊數: xxviii, 924 p. :ill., digital ;24 cm.
    內容註: Prefacing 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 Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering -- Integral Representations and Integral Identities -- Calderón-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 Hölder Spaces -- Layer Potential Operators on Calderón, 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.
    Contained By: Springer Nature eBook
    標題: Divergence theorem. -
    電子資源: https://doi.org/10.1007/978-3-031-05950-6
    ISBN: 9783031059506
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