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The Hodge-Laplacian: boundary value problems on Riemannian manifolds

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Bibliographic Details
Main Authors:	Mitrea, Dorina 1965- (Author), Mitrea, Irina (Author), Mitrea, Marius (Author), Taylor, Michael Eugene 1946- (Author)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2016]
Series:	De Gruyter Studies in Mathematics volume 64
Subjects:	Randwertproblem Laplace-Operator Riemannscher Raum
Links:	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110482669&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029248215&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	ix, 516 Seiten 24 cm x 17 cm
ISBN:	3110482665 9783110482669 9783110484397

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Record in the Search Index

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adam_text	CONTENTS PREFACE 1 1.1 1.2 1.3 1.4 1.5 2 2.1 2.2 2.3 2.4 3 3.1 3.2 3.3 4 4.1 4.2 4.3 5 5.1 5.2 5.3 INTRODUCTION AND STATEMENT OF MAIN RESULTS * 1 FIRST MAIN RESULT: ABSOLUTE AND RELATIVE BOUNDARY CONDITIONS * 3 OTHER PROBLEMS INVOLVING TANGENTIAL AND NORMAL COMPONENTS OF HARMONIC FORMS * 11 BOUNDARY VALUE PROBLEMS FOR HODGE-DIRAC OPERATORS * 21 DIRICHLET, NEUMANN, TRANSMISSION, POINCARE, AND ROBIN-TYPE BOUNDARY PROBLEMS * 24 STRUCTURE OF THE MONOGRAPH * 43 GEOMETRIC CONCEPTS AND TOOLS * 49 DIFFERENTIAL GEOMETRIC PRELIMINARIES * 49 ELEMENTS OF GEOMETRIC MEASURE THEORY * 67 SHARP INTEGRATION BY PARTS FORMULAS FOR DIFFERENTIAL FORMS IN AHLFORS REGULAR DOMAINS * 91 TANGENTIAL AND NORMAL DIFFERENTIAL FORMS ON AHLFORS REGULAR SETS * 96 HARMONIC LAYER POTENTIALS ASSOCIATED WITH THE HODGE-DE RHAM FORMALISM ON UR DOMAINS ----- 109 A FUNDAMENTAL SOLUTION FOR THE HODGE-LAPLACIAN * 109 LAYER POTENTIALS FOR THE HODGE-LAPLACIAN IN THE HODGE-DE RHAM FORMALISM * 117 FREDHOLM THEORY FOR LAYER POTENTIALS IN THE HODGE-DE RHAM FORMALISM * 128 HARMONIC LAYER POTENTIALS ASSOCIATED WITH THE LEVI-CIVITA CONNECTION ON UR DOMAINS * 139 THE DEFINITION AND MAPPING PROPERTIES OF THE DOUBLE LAYER ----- 140 THE DOUBLE LAYER ON UR SUBDOMAINS OF SMOOTH MANIFOLDS * 169 COMPACTNESS OF THE DOUBLE LAYER ON REGULAR SKT DOMAINS * 173 DIRICHLET AND NEUMANN BOUNDARY VALUE PROBLEMS FOR THE HODGE-LAPLACIAN ON REGULAR SKT DOMAINS * 185 FUNCTIONAL ANALYTIC PROPERTIES FOR HARMONIC LAYER POTENTIALS IN UR DOMAINS * 186 INVERTIBILITY RESULTS FOR LAYER POTENTIALS ASSOCIATED WITH THE LEVI-CIVITA CONNECTION * 196 SOLVING THE DIRICHLET, NEUMANN, TRANSMISSION, POINCARE, AND ROBIN BOUNDARY VALUE PROBLEMS * 204 6 6.1 6.2 6.3 7 7.1 7.2 8 8.1 8.2 8.3 8.4 8.5 8.6 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 FATOU THEOREMS AND INTEGRAL REPRESENTATIONS FOR THE HODGE-LAPLACIAN ON REGULAR SKT DOMAINS * 231 CONVERGENCE OF FAMILIES OF SINGULAR INTEGRAL OPERATORS * 231 A FATOU THEOREM FOR THE HODGE-LAPLACIAN IN REGULAR SKT DOMAINS * 250 SPACES OF HARMONIC FIELDS AND GREEN TYPE FORMULAS ----- 261 SOLVABILITY OF BOUNDARY PROBLEMS FOR THE HODGE-LAPLACIAN IN THE HODGE-DE RHAM FORMALISM * 275 PREPARATORY RESULTS * 275 SOLVABILITY RESULTS * 288 ADDITIONAL RESULTS AND APPLICATIONS * 315 DE RHAM COHOMOLOGY ON REGULAR SKT SURFACES * 315 MAXWELLS EQUATIONS IN REGULAR SKT DOMAINS 336 IN REGULAR SKT DOMAINS * 339 FATOU TYPE RESULTS WITH ADDITIONAL CONSTRAINTS OR REGULARITY CONDITIONS * 347 WEAK TANGENTIAL AND NORMAL TRACES IN REGULAR SKT DOMAINS WITH FRIEDRICHS PROPERTY * 352 THE HODGE-POISSON KERNEL AND THE HODGE-HARMONIC MEASURE * 367 FURTHER TOOLS FROM DIFFERENTIAL GEOMETRY, HARMONIC ANALYSIS, GEOMETRIC MEASURE THEORY, FUNCTIONAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, AND CLIFFORD ANALYSIS * 371 CONNECTIONS AND COVARIANT DERIVATIVES ON VECTOR BUNDLES * 371 THE EXTENSION OF THE LEVI-CIVITA CONNECTION TO DIFFERENTIAL FORMS * 381 THE BOCHNER-LAPLACIAN AND WEINTZENBOECKS FORMULA 386 SOBOLEV SPACES ON BOUNDARIES OF AHLFORS REGULAR DOMAINS: THE EUCLIDEAN SETTING * 393 SOBOLEV SPACES ON BOUNDARIES OF AHLFORS REGULAR DOMAINS: THE MANIFOLD SETTING * 408 INTEGRATING BY PARTS ON THE BOUNDARIES OF AHLFORS REGULAR DOMAINS * 417 A GLOBAL SOBOLEV REGULARITY RESULT * 444 THE PV HARMONIC DOUBLE LAYER ON A UR DOMAIN * 446 CALDERON-ZYGMUND THEORY ON UR DOMAINS ON MANIFOLDS * 451 THE FREDHOLMNESS AND INVERTIBILITY OF ELLIPTIC DIFFERENTIAL OPERATORS * 474 COMPACT AND CLOSE-TO-COMPACT SINGULAR INTEGRAL OPERATORS * 482 A SHARP DIVERGENCE THEOREM * 490 9.13 CLIFFORD ANALYSIS RUDIMENTS * 493 9.14 SPECTRAL THEORY FOR UNBOUNDED LINEAR OPERATORS SUBJECT TO CANCELLATIONS * 496 BIBLIOGRAPHY ----- 501 INDEX * 507
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author	Mitrea, Dorina 1965- Mitrea, Irina Mitrea, Marius Taylor, Michael Eugene 1946-
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spellingShingle	Mitrea, Dorina 1965- Mitrea, Irina Mitrea, Marius Taylor, Michael Eugene 1946- The Hodge-Laplacian boundary value problems on Riemannian manifolds De Gruyter Studies in Mathematics Randwertproblem (DE-588)4048395-2 gnd Laplace-Operator (DE-588)4166772-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd
subject_GND	(DE-588)4048395-2 (DE-588)4166772-4 (DE-588)4128295-4
title	The Hodge-Laplacian boundary value problems on Riemannian manifolds
title_auth	The Hodge-Laplacian boundary value problems on Riemannian manifolds
title_exact_search	The Hodge-Laplacian boundary value problems on Riemannian manifolds
title_full	The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea and Michael Taylor
title_fullStr	The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea and Michael Taylor
title_full_unstemmed	The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea and Michael Taylor
title_short	The Hodge-Laplacian
title_sort	the hodge laplacian boundary value problems on riemannian manifolds
title_sub	boundary value problems on Riemannian manifolds
topic	Randwertproblem (DE-588)4048395-2 gnd Laplace-Operator (DE-588)4166772-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd
topic_facet	Randwertproblem Laplace-Operator Riemannscher Raum
url	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110482669&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029248215&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000005407
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