LEADER 04267nam 2200577 450 001 9910798732003321 005 20230808195829.0 010 $a3-11-048339-4 010 $a3-11-048438-2 024 7 $a10.1515/9783110484380 035 $a(CKB)3710000000887292 035 $a(MiAaPQ)EBC4707943 035 $a(DE-B1597)467372 035 $a(OCoLC)960041744 035 $a(OCoLC)962087347 035 $a(DE-B1597)9783110484380 035 $a(Au-PeEL)EBL4707943 035 $a(CaPaEBR)ebr11274572 035 $a(CaONFJC)MIL957926 035 $a(EXLCZ)993710000000887292 100 $a20161014h20162016 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 04$aThe Hodge-Laplacian $eboundary value problems on Riemannian manifolds /$fDorina Mitrea [and three others] 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2016. 210 4$d©2016 215 $a1 online resource (528 pages) 225 1 $aDe Gruyter Studies in Mathematics,$x0179-0986 ;$vVolume 64 311 $a3-11-048266-5 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPreface -- $tContents -- $t1. Introduction and Statement of Main Results -- $t2. Geometric Concepts and Tools -- $t3. Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains -- $t4. Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains -- $t5. Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains -- $t6. Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains -- $t7. Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism -- $t8. Additional Results and Applications -- $t9. Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis -- $tBibliography -- $tIndex -- $tBackmatter 330 $aThe core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains.Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents:PrefaceIntroduction and Statement of Main ResultsGeometric Concepts and ToolsHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR DomainsHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR DomainsDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT DomainsFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT DomainsSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham FormalismAdditional Results and ApplicationsFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford AnalysisBibliographyIndex 410 0$aDe Gruyter studies in mathematics ;$vVolume 64. 606 $aRiemannian manifolds 606 $aBoundary value problems 615 0$aRiemannian manifolds. 615 0$aBoundary value problems. 676 $a516.3/73 686 $aSK 540$2rvk 700 $aMitrea$b Dorina, $0521700 702 $aMitrea$b Dorina$f1965- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910798732003321 996 $aThe Hodge-Laplacian$93721641 997 $aUNINA