LEADER 03312nam 22005175 450 001 9910741186503321 005 20230822052810.0 010 $a3-031-31561-8 024 7 $a10.1007/978-3-031-31561-9 035 $a(CKB)28013438300041 035 $a(MiAaPQ)EBC30718776 035 $a(Au-PeEL)EBL30718776 035 $a(DE-He213)978-3-031-31561-9 035 $a(PPN)272260606 035 $a(EXLCZ)9928013438300041 100 $a20230822d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Harmonic Analysis V$b[electronic resource] $eFredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems /$fby Dorina Mitrea, Irina Mitrea, Marius Mitrea 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (1006 pages) 225 1 $aDevelopments in Mathematics,$x2197-795X ;$v76 311 $a9783031315602 320 $aIncludes bibliographical references. 327 $aIntroduction 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. 330 $aThis monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations.The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations. 410 0$aDevelopments in Mathematics,$x2197-795X ;$v76 606 $aMathematical analysis 606 $aIntegral Transforms and Operational Calculus 615 0$aMathematical analysis. 615 14$aIntegral Transforms and Operational Calculus. 676 $a515.42 700 $aMitrea$b Dorina$f1965-$01171699 702 $aMitrea$b Irina 702 $aMitrea$b Marius 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910741186503321 996 $aGeometric harmonic analysis V$93555317 997 $aUNINA