LEADER 03499nam 22005655 450 001 9910725088003321 005 20240117155812.0 010 $a9783031227356$b(electronic bk.) 010 $z9783031227349 024 7 $a10.1007/978-3-031-22735-6 035 $a(MiAaPQ)EBC7248830 035 $a(Au-PeEL)EBL7248830 035 $a(DE-He213)978-3-031-22735-6 035 $a(BIP)086286147 035 $a(PPN)270612653 035 $a(EXLCZ)9926637879900041 100 $a20230512d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Harmonic Analysis III$b[electronic resource] $eIntegral Representations, Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering /$fby Dorina Mitrea, Irina Mitrea, Marius Mitrea 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (980 pages) 225 1 $aDevelopments in Mathematics,$x2197-795X ;$v74 311 08$aPrint version: Mitrea, Dorina Geometric Harmonic Analysis III Cham : Springer International Publishing AG,c2023 9783031227349 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 $aThis monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderón-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors. 410 0$aDevelopments in Mathematics,$x2197-795X ;$v74 606 $aMathematical analysis 606 $aIntegral Transforms and Operational Calculus 606 $aTeoria de la mesura geomètrica$2thub 608 $aLlibres electrònics$2thub 610 $aMathematics 615 0$aMathematical analysis. 615 14$aIntegral Transforms and Operational Calculus. 615 7$aTeoria de la mesura geomètrica 676 $a515.4 700 $aMitrea$b Dorina$f1965-$01171699 702 $aMitrea$b Irina 702 $aMitrea$b Marius 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910725088003321 996 $aGeometric Harmonic Analysis III$93566859 997 $aUNINA