Polyharmonic boundary value problems: positivity preserving and nonlinear higher order elliptic equations in bounded domains
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Series: | Lecture Notes in Mathematics
1991 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVIII, 423 S. Ill., graph. Darst. |
| ISBN: | 9783642122446 |
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MARC
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| 245 | 1 | 0 | |a Polyharmonic boundary value problems |b positivity preserving and nonlinear higher order elliptic equations in bounded domains |c Filippo Gazzola ; Hans-Christoph Grunau ; Guido Sweers |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XVIII, 423 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1991 | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text |
CONTENTS PREFACE VII ACKNOWLEDGEMENTS XIII 1 MODELS OF HIGHER ORDER 1
1.1 CLASSICAL PROBLEMS FROM ELASTICITY 1 1.1.1 THE STATIC LOADING OF A
SLENDER BEAM 2 1.1.2 THE KIRCHHOFF-LOVE MODEL FOR A THIN PLATE 5 1.1.3
DECOMPOSITION INTO SECOND ORDER SYSTEMS 8 1.2 THE BOGGIO-HADAMARD
CONJECTURE FOR A CLAMPED PLATE 9 1.3 THE FIRST EIGENVALUE 12 1.3.1 THE
DIRICHLET EIGENVALUE PROBLEM 13 1.3.2 AN EIGENVALUE PROBLEM FOR A
BUCKLED PLATE 14 1.3.3 A STEKLOV EIGENVALUE PROBLEM 15 1.4 PARADOXES FOR
THE HINGED PLATE 16 1.4.1 SAPONDZYAN'S PARADOX BY CONCAVE CORNERS 17
1.4.2 THE BABUSKA PARADOX 17 1.5 PANEITZ-BRANSON TYPE EQUATIONS 18 1.6
CRITICAL GROWTH POLYHARMONIC MODEL PROBLEMS 21 1.7 QUALITATIVE
PROPERTIES OF SOLUTIONS TO SEMILINEAR PROBLEMS 22 1.8 WILLMORE SURFACES
23 2 LINEAR PROBLEMS 27 2. 1 POLYHARMONIC OPERATORS 27 2.2 HIGHER ORDER
SOBOLEV SPACES 29 2.2.1 DEFINITIONS AND BASIC PROPERTIES 29 2.2.2
EMBEDDING THEOREMS 32 2.3 BOUNDARY CONDITIONS 33 2.4 HUBERT SPACE THEORY
36 2.4.1 NORMAL BOUNDARY CONDITIONS AND GREEN'S FORMULA 36 2.4.2
HOMOGENEOUS BOUNDARY VALUE PROBLEMS 38 2.4.3 INHOMOGENEOUS BOUNDARY
VALUE PROBLEMS 42 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1000569101 DIGITALISIERT DURCH XVI CONTENTS 2.5
REGULARITY RESULTS AND A PRIORI ESTIMATES 44 2.5.1 SCHAUDER THEORY 44
2.5.2 //-THEORY 46 2.5.3 THE MIRANDA-AGMON MAXIMUM MODULUS ESTIMATES 48
2.6 GREEN'S FUNCTION AND BOGGIO'S FORMULA 50 2.7 THE SPACE H 2 N H AND
THE SAPONDZYAN-BABUSKA PARADOXES 52 2.8 BIBLIOGRAPHICAL NOTES 59 3
EIGENVALUE PROBLEMS 61 3.1 DIRICHLET EIGENVALUES 62 3.1.1 A GENERALISED
KREIN-RUTMAN RESULT 62 3.1.2 DECOMPOSITION WITH RESPECT TO DUAL CONES 63
3.1.3 POSITIVITY OF THE FIRST EIGENFUNCTION 68 3.1.4 SYMMETRISATION AND
TALENTI'S COMPARISON PRINCIPLE 71 3.1.5 THE RAYLEIGH CONJECTURE FOR THE
CLAMPED PLATE 73 3.2 BUCKLING LOAD OF A CLAMPED PLATE 77 3.3 STEKLOV
EIGENVALUES 82 3.3.1 THE STEKLOV SPECTRUM 83 3.3.2 MINIMISATION OF THE
FIRST EIGENVALUE 90 3.4 BIBLIOGRAPHICAL NOTES 96 4 KERNEL ESTIMATES 99
4. 1 CONSEQUENCES OF BOGGIO'S FORMULA 99 4.2 KERNEL ESTIMATES IN THE
BALL 101 4.2.1 DIRECT GREEN FUNCTION ESTIMATES 101 4.2.2 A 3-G-TYPE
THEOREM 110 4.3 ESTIMATES FOR THE STEKLOV PROBLEM 116 4.4 GENERAL
PROPERTIES OF THE GREEN FUNCTIONS 122 4.4.1 REGULARITY OF THE BIHARMONIC
GREEN FUNCTION 122 4.4.2 PRELIMINARY ESTIMATES FOR THE GREEN FUNCTION
123 4.5 UNIFORM GREEN FUNCTIONS ESTIMATES IN C 4 R CONTENTS XVII 5.4
STEKLOV BOUNDARY CONDITIONS 167 5.4.1 POSITIVITY PRESERVING 168 5.4.2
POSITIVITY OF THE OPERATORS INVOLVED IN THE STEKLOV PROBLEM 175 5.4.3
RELATION BETWEEN HUBERT AND SCHAUDER SETTING 178 5.5 BIBLIOGRAPHICAL
NOTES 1 85 6 DOMINANCE OF POSITIVITY IN LINEAR EQUATIONS 187 6.1 HIGHEST
ORDER PERTURBATIONS IN TWO DIMENSIONS 188 6.1.1 DOMAIN PERTURBATIONS 190
6.1.2 PERTURBATIONS OF THE PRINCIPAL PART 193 6.2 SMALL NEGATIVE PART OF
BIHARMONIC GREEN'S FUNCTIONS IN TWO DIMENSIONS 197 6.2.1 THE BIHARMONIC
GREEN FUNCTION ON THE LIMACONS DE PASCAL 197 6.2.2 FILLING SMOOTH
DOMAINS WITH PERTURBED LIMACONS 201 6.3 REGIONS OF POSITIVITY IN
ARBITRARY DOMAINS IN HIGHER DIMENSIONS. .208 6.3.1 THE BIHARMONIC
OPERATOR 210 6.3.2 EXTENSIONS TO POLYHARMONIC OPERATORS 215 6.4 SMALL
NEGATIVE PART OF BIHARMONIC GREEN'S FUNCTIONS IN HIGHER DIMENSIONS 216
6.4.1 BOUNDS FOR THE NEGATIVE PART 217 6.4.2 A BLOW-UP PROCEDURE 218 6.5
DOMAIN PERTURBATIONS IN HIGHER DIMENSIONS 224 6.6 BIBLIOGRAPHICAL NOTES
226 7 SEMILINEAR PROBLEMS 227 7.1 A GIDAS-NI-NIRENBERG TYPE SYMMETRY
RESULT 229 7.1.1 GREEN FUNCTION INEQUALITIES 231 7.1.2 THE MOVING PLANE
ARGUMENT 234 7.2 A BRIEF OVERVIEW OF SUBCRITICAL PROBLEMS 238 7.2.1
REGULARITY FOR AT MOST CRITICAL GROWTH PROBLEMS 238 7.2. XVIII CONTENTS
7.9 CRITICAL GROWTH PROBLEMS IN GEOMETRICALLY COMPLICATED DOMAINS . .300
7.9.1 EXISTENCE RESULTS IN DOMAINS WITH NONTRIVIAL TOPOLOGY . 301
7.9.2 EXISTENCE RESULTS IN CONTRACTIBLE DOMAINS 302 7.9.3 ENERGY OF
NODAL SOLUTIONS 304 7.9.4 THE DEFORMATION ARGUMENT 307 7.9.5 A
STRUWE-TYPE COMPACTNESS RESULT 311 7.10 THE CONFORMALLY COVARIANT
PANEITZ EQUATION IN HYPERBOLIC SPACE 319 7.10.1 INFINITELY MANY COMPLETE
RADIAL CONFORMAI METRICS WITH THE SAME Q-CURVATURE 319 7.10.2 EXISTENCE
AND NEGATIVE SCALAR CURVATURE 320 7.10.3 COMPLETENESS OF THE CONFORMAI
METRIC 326 7.11 FOURTH ORDER EQUATIONS WITH SUPERCRITICAL TERMS 335
7.11.1 AN AUTONOMOUS SYSTEM 339 7.11.2 REGULAR MINIMAL SOLUTIONS 347
7.11.3 CHARACTERISATION OF SINGULAR SOLUTIONS 352 7.11.4 STABILITY OF
THE MINIMAL REGULAR SOLUTION 357 7.11.5 EXISTENCE AND UNIQUENESS OF A
SINGULAR SOLUTION 360 7.12 BIBLIOGRAPHICAL NOTES 366 8 WILLMORE SURFACES
OF REVOLUTION 371 8.1 AN EXISTENCE RESULT 371 8.2 GEOMETRIC BACKGROUND
372 8.2.1 GEOMETRIC QUANTITIES FOR SURFACES OF REVOLUTION 372 8.2.2
SURFACES OF REVOLUTION AS ELASTIC CURVES IN THE HYPERBOLIC HALF PLANE
376 8.3 MINIMISATION OF THE WILLMORE FUNCTIONAL 381 8.3.1 AN UPPER BOUND
FOR THE OPTIMAL ENERGY 382 8.3.2 MONOTONICITY OF THE OPTIMAL ENERGY 383
8.3.3 PROPERTIES OF MINIMISING SEQUENCES 387 8.3.4 ATTAINMENT OF THE
MINIMAL ENERGY 389 8. |
| any_adam_object | 1 |
| author | Gazzola, Filippo Grunau, Hans-Christoph 1961- Sweers, Guido |
| author_GND | (DE-588)123905133 (DE-588)121265315 (DE-588)111529840 |
| author_facet | Gazzola, Filippo Grunau, Hans-Christoph 1961- Sweers, Guido |
| author_role | aut aut aut |
| author_sort | Gazzola, Filippo |
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| building | Verbundindex |
| bvnumber | BV036516308 |
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| dewey-full | 515.3533 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3533 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| spelling | Gazzola, Filippo Verfasser (DE-588)123905133 aut Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains Filippo Gazzola ; Hans-Christoph Grunau ; Guido Sweers Berlin [u.a.] Springer 2010 XVIII, 423 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1991 Randwertproblem (DE-588)4048395-2 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Ordnung n (DE-588)4322729-6 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s Ordnung n (DE-588)4322729-6 s Randwertproblem (DE-588)4048395-2 s DE-604 Grunau, Hans-Christoph 1961- Verfasser (DE-588)121265315 aut Sweers, Guido Verfasser (DE-588)111529840 aut Erscheint auch als Online-Ausgabe 978-3-642-12245-3 Lecture Notes in Mathematics 1991 (DE-604)BV000676446 1991 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3435217&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020438413&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gazzola, Filippo Grunau, Hans-Christoph 1961- Sweers, Guido Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains Lecture Notes in Mathematics Randwertproblem (DE-588)4048395-2 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd Ordnung n (DE-588)4322729-6 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4310554-3 (DE-588)4322729-6 |
| title | Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains |
| title_auth | Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains |
| title_exact_search | Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains |
| title_full | Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains Filippo Gazzola ; Hans-Christoph Grunau ; Guido Sweers |
| title_fullStr | Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains Filippo Gazzola ; Hans-Christoph Grunau ; Guido Sweers |
| title_full_unstemmed | Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains Filippo Gazzola ; Hans-Christoph Grunau ; Guido Sweers |
| title_short | Polyharmonic boundary value problems |
| title_sort | polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains |
| title_sub | positivity preserving and nonlinear higher order elliptic equations in bounded domains |
| topic | Randwertproblem (DE-588)4048395-2 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd Ordnung n (DE-588)4322729-6 gnd |
| topic_facet | Randwertproblem Nichtlineare elliptische Differentialgleichung Ordnung n |
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