The Maz'ya anniversary collection: 1 On Maz'ya's work in functional analysis, partial differential equations and applications
Gespeichert in:
| Körperschaft: | |
|---|---|
| Format: | Tagungsbericht Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1999
|
| Schriftenreihe: | Operator theory advances and applications
109 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Bibliogr. Vladimir Maz'ya S. [335] - 364 |
| Beschreibung: | 364 S. graph. Darst. |
| ISBN: | 3764362014 0817662014 |
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| 111 | 2 | |a Conference in Honour of Vladimir Mazya |d 1998 |c Rostock |j Verfasser |0 (DE-588)2173758-7 |4 aut | |
| 245 | 1 | 0 | |a The Maz'ya anniversary collection |n 1 |p On Maz'ya's work in functional analysis, partial differential equations and applications |c Jürgen Rossmann ... (eds.) |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1999 | |
| 300 | |a 364 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory advances and applications |v 109 | |
| 490 | 0 | |a Operator theory advances and applications |v ... | |
| 500 | |a Bibliogr. Vladimir Maz'ya S. [335] - 364 | ||
| 700 | 1 | |a Roßmann, Jürgen |e Sonstige |4 oth | |
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| 830 | 0 | |a Operator theory advances and applications |v 109 |w (DE-604)BV000000970 | |
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Datensatz im Suchindex
| _version_ | 1804136066010054656 |
|---|---|
| adam_text | Contents
G. WlLDENHAIN
Introduction ix
I. GOHBERG
Vladimir Maz ya: Friend and mathematician. Recollections 1
L. I. Hedberg
On Maz ya s work in potential theory and the theory of function spaces 7
1. Introduction 7
2. Embeddings and isoperimetric inequalities 7
3. Regularity of solutions 10
4. Boundary regularity 11
5. Nonlinear potential theory 12
N. G. Kuznetsov and B. R. Vainberg
Maz ya s works in the linear theory of water waves 17
1. Introduction 17
2. The unique solvability of the water wave problem 18
3. The Neumann Kelvin problem 25
4. Asymptotic expansions for transient water waves due to brief and
high frequency disturbances 28
J. Elschner
Maz ya s work on integral and pseudodifferential operators 35
1. Non elliptic operators 35
2. Oblique derivative problem: breakthrough in the generic case of
degeneration 37
3. Estimates for differential operators in the half space 39
4. The characteristic Cauchy problem for hyperbolic equations 40
5. New methods for solving ill posed boundary value problems 42
6. Applications of multiplier theory to integral operators 42
7. Integral equations of harmonic potential theory on general
non regular surfaces 43
8. Boundary integral equations on piecewise smooth surfaces 45
J. ROSSMANN
Contributions of V. Maz ya to the theory of boundary value problems in
nonsmooth domains 53
1. Maz ya s early work on boundary value problems in
nonsmooth domains 54
viii Contents
2. General elliptic boundary value problems in domains with point
singularities 65
3. Boundary value problems in domains with edges 77
4. Spectral properties of operator pencils generated by elliptic boundary
value problems in a cone 83
5. Applications to elastostatics and hydrodynamics 86
6. Singularities of solutions to nonlinear elliptic equations at
a cone vertex 91
V. Havin
On some potential theoretic themes in function theory 99
1. Approximation theory 99
2. Uniqueness properties of analytic functions 103
3. The Cauchy problem for the Laplace equation 105
G. Schmidt
Approximate approximations and their applications 1ll
1. Introduction 1ll
2. Quasi interpolation 113
3. Generating functions for quasi interpolation of high order 117
4. Semi analytic cubature formulas 120
5. Cubature of integral operators over bounded domains 122
6. Approximate wavelets 126
7. Numerical algorithms based upon approximate approximations 130
R. Cooke
Maz ya s work on the biography of Hadamard 137
A. GriGORYAN
Isoperimetric inequalities and capacities on Riemannian manifolds 139
1. Introduction 139
2. Capacity of balls 141
3. Parabolicity of manifolds 143
4. Isoperimetric inequality and Sobolev inequality 145
5. Capacity and the principal frequency 145
6. Cheeger s inequality 147
7. Eigenvalues of balls on spherically symmetric manifolds 148
8. Heat kernel on spherically symmetric manifolds 149
T. Shaposhnikova
Multipliers of differentiable functions and their traces 155
1. Introduction 155
2. Description and properties of multipliers 156
3. Multipliers in the space of Bessel potentials as traces
of multipliers 162
Contents ix
V. A. Kozlov
An asymptotic theory of nonlinear abstract higher order ordinary
differential equations 171
S. POBORCHI
Sobolev spaces for domains with cusps 175
1. Introduction 175
2. Extension theorems 176
3. Embedding theorems 179
4. Boundary values of Sobolev functions 181
V. BURENKOV
Extension theorems for Sobolev spaces 187
1. Introduction ) 187
2. Extensions with preservation of class 188
3. Estimates for the minimal norm of an extension operator 190
4. Extensions with deterioration of class 193
A. MOVCHAN
Contributions of V.G. Maz ya to analysis of singularly perturbed
boundary value problems 201
1. Introduction 201
2. Domain with a small hole 202
3. General asymptotic theory by Maz ya, Nazarov and Plamenevskii 206
4. Asymptotics of solutions of boundary integral equations under a small
perturbation of a corner 207
5. Compound asymptotics for homogenization problems 208
6. Boundary value problems in 3D 1D multi structures 210
J. ASLUND
Asymptotic analysis of a mixed boundary value problem in
a singularly degenerating domain 213
1. Introduction 213
2. Formulation of the problem 213
3. The leading order approximation 215
A. Kozhevnikov
A history of the Cosserat spectrum 223
1. Introduction 223
2. The first boundary value problem of elastostatics 224
3. The second and other boundary value problems 227
4. Applications and other related results 230
x Contents
A. SOLOVIEV
Boundary integral equations for plane domains with cusps 235
1. Introduction 235
2. Integral equations in weighted Sobolev spaces 237
S. Eilertsen
On Maz ya type inequalities for convolution operators 243
1. Introduction 243
2. One dimensional polynomials 244
3. The functions x 2X in M.n 246
G. Kresin
Sharp constants and maximum principles for elliptic and parabolic systems
with continuous boundary data 249
1. The norm and the essential norm of the double layer elastic and
hydrodynamic potentials in the space of continuous functions 253
2. Exact constants in inequalities of maximum principle type for certain
systems and equations of mathematical physics 264
3. Maximum modulus principle for elliptic systems 270
4. Maximum modulus principle for parabolic systems 278
5. Maximum norm principle for parabolic systems 287
M. Langer
Lp contractivity of semigroups generated by parabolic
matrix differential operators 307
1. Introduction 307
2. Preliminaries 310
3. Weakly coupled systems 311
4. Coupled systems 322
Curriculum vitae of Vladimir Maz ya 331
Publications of Vladimir Maz ya 335
|
| adam_txt |
Contents
G. WlLDENHAIN
Introduction ix
I. GOHBERG
Vladimir Maz'ya: Friend and mathematician. Recollections 1
L. I. Hedberg
On Maz'ya's work in potential theory and the theory of function spaces 7
1. Introduction 7
2. Embeddings and isoperimetric inequalities 7
3. Regularity of solutions 10
4. Boundary regularity 11
5. Nonlinear potential theory 12
N. G. Kuznetsov and B. R. Vainberg
Maz'ya's works in the linear theory of water waves 17
1. Introduction 17
2. The unique solvability of the water wave problem 18
3. The Neumann Kelvin problem 25
4. Asymptotic expansions for transient water waves due to brief and
high frequency disturbances 28
J. Elschner
Maz'ya's work on integral and pseudodifferential operators 35
1. Non elliptic operators 35
2. Oblique derivative problem: breakthrough in the generic case of
degeneration 37
3. Estimates for differential operators in the half space 39
4. The characteristic Cauchy problem for hyperbolic equations 40
5. New methods for solving ill posed boundary value problems 42
6. Applications of multiplier theory to integral operators 42
7. Integral equations of harmonic potential theory on general
non regular surfaces 43
8. Boundary integral equations on piecewise smooth surfaces 45
J. ROSSMANN
Contributions of V. Maz'ya to the theory of boundary value problems in
nonsmooth domains 53
1. Maz'ya's early work on boundary value problems in
nonsmooth domains 54
viii Contents
2. General elliptic boundary value problems in domains with point
singularities 65
3. Boundary value problems in domains with edges 77
4. Spectral properties of operator pencils generated by elliptic boundary
value problems in a cone 83
5. Applications to elastostatics and hydrodynamics 86
6. Singularities of solutions to nonlinear elliptic equations at
a cone vertex 91
V. Havin
On some potential theoretic themes in function theory 99
1. Approximation theory 99
2. Uniqueness properties of analytic functions 103
3. The Cauchy problem for the Laplace equation 105
G. Schmidt
Approximate approximations and their applications 1ll
1. Introduction 1ll
2. Quasi interpolation 113
3. Generating functions for quasi interpolation of high order 117
4. Semi analytic cubature formulas 120
5. Cubature of integral operators over bounded domains 122
6. Approximate wavelets 126
7. Numerical algorithms based upon approximate approximations 130
R. Cooke
Maz'ya's work on the biography of Hadamard 137
A. GriGORYAN
Isoperimetric inequalities and capacities on Riemannian manifolds 139
1. Introduction 139
2. Capacity of balls 141
3. Parabolicity of manifolds 143
4. Isoperimetric inequality and Sobolev inequality 145
5. Capacity and the principal frequency 145
6. Cheeger's inequality 147
7. Eigenvalues of balls on spherically symmetric manifolds 148
8. Heat kernel on spherically symmetric manifolds 149
T. Shaposhnikova
Multipliers of differentiable functions and their traces 155
1. Introduction 155
2. Description and properties of multipliers 156
3. Multipliers in the space of Bessel potentials as traces
of multipliers 162
Contents ix
V. A. Kozlov
An asymptotic theory of nonlinear abstract higher order ordinary
differential equations 171
S. POBORCHI
Sobolev spaces for domains with cusps 175
1. Introduction 175
2. Extension theorems 176
3. Embedding theorems 179
4. Boundary values of Sobolev functions 181
V. BURENKOV
Extension theorems for Sobolev spaces 187
1. Introduction ) 187
2. Extensions with preservation of class 188
3. Estimates for the minimal norm of an extension operator 190
4. Extensions with deterioration of class 193
A. MOVCHAN
Contributions of V.G. Maz'ya to analysis of singularly perturbed
boundary value problems 201
1. Introduction 201
2. Domain with a small hole 202
3. General asymptotic theory by Maz'ya, Nazarov and Plamenevskii 206
4. Asymptotics of solutions of boundary integral equations under a small
perturbation of a corner 207
5. Compound asymptotics for homogenization problems 208
6. Boundary value problems in 3D 1D multi structures 210
J. ASLUND
Asymptotic analysis of a mixed boundary value problem in
a singularly degenerating domain 213
1. Introduction 213
2. Formulation of the problem 213
3. The leading order approximation 215
A. Kozhevnikov
A history of the Cosserat spectrum 223
1. Introduction 223
2. The first boundary value problem of elastostatics 224
3. The second and other boundary value problems 227
4. Applications and other related results 230
x Contents
A. SOLOVIEV
Boundary integral equations for plane domains with cusps 235
1. Introduction 235
2. Integral equations in weighted Sobolev spaces 237
S. Eilertsen
On Maz'ya type inequalities for convolution operators 243
1. Introduction 243
2. One dimensional polynomials 244
3. The functions \x\2X in M.n 246
G. Kresin
Sharp constants and maximum principles for elliptic and parabolic systems
with continuous boundary data 249
1. The norm and the essential norm of the double layer elastic and
hydrodynamic potentials in the space of continuous functions 253
2. Exact constants in inequalities of maximum principle type for certain
systems and equations of mathematical physics 264
3. Maximum modulus principle for elliptic systems 270
4. Maximum modulus principle for parabolic systems 278
5. Maximum norm principle for parabolic systems 287
M. Langer
Lp contractivity of semigroups generated by parabolic
matrix differential operators 307
1. Introduction 307
2. Preliminaries 310
3. Weakly coupled systems 311
4. Coupled systems 322
Curriculum vitae of Vladimir Maz'ya 331
Publications of Vladimir Maz'ya 335 |
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| spelling | Conference in Honour of Vladimir Mazya 1998 Rostock Verfasser (DE-588)2173758-7 aut The Maz'ya anniversary collection 1 On Maz'ya's work in functional analysis, partial differential equations and applications Jürgen Rossmann ... (eds.) Basel [u.a.] Birkhäuser 1999 364 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Operator theory advances and applications 109 Operator theory advances and applications ... Bibliogr. Vladimir Maz'ya S. [335] - 364 Roßmann, Jürgen Sonstige oth (DE-604)BV021860403 1 Operator theory advances and applications 109 (DE-604)BV000000970 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015305575&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The Maz'ya anniversary collection Operator theory advances and applications |
| title | The Maz'ya anniversary collection |
| title_auth | The Maz'ya anniversary collection |
| title_exact_search | The Maz'ya anniversary collection |
| title_exact_search_txtP | The Maz'ya anniversary collection |
| title_full | The Maz'ya anniversary collection 1 On Maz'ya's work in functional analysis, partial differential equations and applications Jürgen Rossmann ... (eds.) |
| title_fullStr | The Maz'ya anniversary collection 1 On Maz'ya's work in functional analysis, partial differential equations and applications Jürgen Rossmann ... (eds.) |
| title_full_unstemmed | The Maz'ya anniversary collection 1 On Maz'ya's work in functional analysis, partial differential equations and applications Jürgen Rossmann ... (eds.) |
| title_short | The Maz'ya anniversary collection |
| title_sort | the maz ya anniversary collection on maz ya s work in functional analysis partial differential equations and applications |
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