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Titel:	Spectral problems associated with corner singularities of solutions to elliptic equations
Von:	V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann
Person:	Kozlov, Vladimir 1954- Verfasser aut Mazʹja, Vladimir Gilelevič Roßmann, Jürgen 1937-
Hauptverfassende:	Kozlov, Vladimir 1954- (VerfasserIn), Mazʹja, Vladimir Gilelevič 1937- (VerfasserIn), Roßmann, Jürgen 1954- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Providence, Rhode Island American Mathematical Society [2001]
Schriftenreihe:	Mathematical surveys and monographs Volume 85
Notation:	SK 920 SK 560
Schlagwörter:	Mathematische Physik Boundary value problems > Numerical solutions Differential equations, Elliptic > Numerical solutions Mathematical physics Singularities (Mathematics) Singularität > Mathematik Randwertproblem Elliptische Differentialgleichung Numerisches Verfahren
Medienzugang:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009500044&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	ix, 436 Seiten
ISBN:	0821827278 9780821827277

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adam_text	Contents Introduction 1 Part 1. Singularities of solutions to equations of mathematical physics 7 Chapter 1. Prerequisites on operator pencils 9 1.1. Operator pencils 10 1.2. Operator pencils corresponding to sesquilinear forms 15 1.3. A variational principle for operator pencils 21 1.4. Elliptic boundary value problems in domains with conic points: some basic results 26 1.5. Notes 31 Chapter 2. Angle and conic singularities of harmonic functions 35 2.1. Boundary value problems for the Laplace operator in an angle 36 2.2. The Dirichlet problem for the Laplace operator in a cone 40 2.3. The Neumann problem for the Laplace operator in a cone 45 2.4. The problem with oblique derivative 49 2.5. Further results 52 2.6. Applications to boundary value problems for the Laplace equation 54 2.7. Notes 57 Chapter 3. The Dirichlet problem for the Lame system 61 3.1. The Dirichlet problem for the Lame system in a plane angle 64 3.2. The operator pencil generated by the Dirichlet problem in a cone 74 3.3. Properties of real eigenvalues 83 3.4. The set functions T and Fv 88 3.5. A variational principle for real eigenvalues 91 3.6. Estimates for the width of the energy strip 93 3.7. Eigenvalues for circular cones 97 3.8. Applications 100 3.9. Notes 105 Chapter 4. Other boundary value problems for the Lame system 107 4.1. A mixed boundary value problem for the Lame system 108 4.2. The Neumann problem for the Lame system in a plane angle 120 4.3. The Neumann problem for the Lame system in a cone 125 4.4. Angular crack in an anisotropic elastic space 133 4.5. Notes 138 Chapter 5. The Dirichlet problem for the Stokes system 139 vii viii CONTENTS 5.1. The Dirichlet problem for the Stokes system in an angle 142 5.2. The operator pencil generated by the Dirichlet problem in a cone 148 5.3. Properties of real eigenvalues 155 5.4. The eigenvalues A=l and A = 2 159 5.5. A variational principle for real eigenvalues 168 5.6. Eigenvalues in the case of right circular cones 175 5.7. The Dirichlet problem for the Stokes system in a dihedron 178 5.8. Stokes and Navier Stokes systems in domains with piecewise smooth boundaries 192 5.9. Notes 196 Chapter 6. Other boundary value problems for the Stokes system in a cone 199 6.1. A mixed boundary value problem for the Stokes system 200 6.2. Real eigenvalues of the pencil to the mixed problem 212 6.3. The Neumann problem for the Stokes system 223 6.4. Notes 225 Chapter 7. The Dirichlet problem for the biharmonic and polyharmonic equations 227 7.1. The Dirichlet problem for the biharmonic equation in an angle 229 7.2. The Dirichlet problem for the biharmonic equation in a cone 233 7.3. The polyharmonic operator 239 7.4. The Dirichlet problem for A2 in domains with piecewise smooth boundaries 246 7.5. Notes 248 Part 2. Singularities of solutions to general elliptic equations and systems 251 Chapter 8. The Dirichlet problem for elliptic equations and systems in an angle 253 8.1. The operator pencil generated by the Dirichlet problem 254 8.2. An asymptotic formula for the eigenvalue close to m 263 8.3. Asymptotic formulas for the eigenvalues close torn 1/2 265 8.4. The case of a convex angle 272 8.5. The case of a nonconvex angle 275 8.6. The Dirichlet problem for a second order system 283 8.7. Applications 286 8.8. Notes 291 Chapter 9. Asymptotics of the spectrum of operator pencils generated by general boundary value problems in an angle 293 9.1. The operator pencil generated by a regular boundary value problem 293 9.2. Distribution of the eigenvalues 299 9.3. Notes 305 Chapter 10. The Dirichlet problem for strongly elliptic systems in particular cones 307 10.1. Basic properties of the operator pencil generated by the Dirichlet problem 308 CONTENTS ix 10.2. Elliptic systems in Rn 313 10.3. The Dirichlet problem in the half space 319 10.4. The Sobolev problem in the exterior of a ray 321 10.5. The Dirichlet problem in a dihedron 332 10.6. Notes 344 Chapter 11. The Dirichlet problem in a cone 345 11.1. The case of a "smooth" cone 346 11.2. The case of a nonsmooth cone 350 11.3. Second order systems 353 11.4. Second order systems in a polyhedral cone 365 11.5. Exterior of a thin cone 368 11.6. A cone close to the half space 376 11.7. Nonrealness of eigenvalues 383 11.8. Further results 384 11.9. The Dirichlet problem in domains with conic vertices 386 11.10. Notes 387 Chapter 12. The Neumann problem in a cone 389 12.1. The operator pencil generated by the Neumann problem 391 12.2. The energy line 396 12.3. The energy strip 398 12.4. Applications to the Neumann problem in a bounded domain 411 12.5. The Neumann problem for anisotropic elasticity in an angle 414 12.6. Notes 415 Bibliography 417 Index 429 List of Symbols 433
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indexdate	2025-04-15T08:00:59Z
institution	BVB
isbn	0821827278 9780821827277
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009500044
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series	Mathematical surveys and monographs
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spellingShingle	Kozlov, Vladimir 1954- Mazʹja, Vladimir Gilelevič 1937- Roßmann, Jürgen 1954- Spectral problems associated with corner singularities of solutions to elliptic equations Mathematical surveys and monographs Mathematische Physik Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Mathematical physics Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
subject_GND	(DE-588)4077459-4 (DE-588)4048395-2 (DE-588)4014485-9 (DE-588)4128130-5
title	Spectral problems associated with corner singularities of solutions to elliptic equations
title_auth	Spectral problems associated with corner singularities of solutions to elliptic equations
title_exact_search	Spectral problems associated with corner singularities of solutions to elliptic equations
title_full	Spectral problems associated with corner singularities of solutions to elliptic equations V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann
title_fullStr	Spectral problems associated with corner singularities of solutions to elliptic equations V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann
title_full_unstemmed	Spectral problems associated with corner singularities of solutions to elliptic equations V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann
title_short	Spectral problems associated with corner singularities of solutions to elliptic equations
title_sort	spectral problems associated with corner singularities of solutions to elliptic equations
topic	Mathematische Physik Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Mathematical physics Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
topic_facet	Mathematische Physik Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Mathematical physics Singularities (Mathematics) Singularität Mathematik Randwertproblem Elliptische Differentialgleichung Numerisches Verfahren
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009500044&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000018014
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