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The Resource The Maz'ya Anniversary Collection : Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications, edited by Jürgen Rossmann, Peter Takáč, Günther Wildenhain, (electronic resource)

The Maz'ya Anniversary Collection : Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications, edited by Jürgen Rossmann, Peter Takáč, Günther Wildenhain, (electronic resource)

Label
The Maz'ya Anniversary Collection : Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications
Title
The Maz'ya Anniversary Collection
Title remainder
Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications
Statement of responsibility
edited by Jürgen Rossmann, Peter Takáč, Günther Wildenhain
Creator
Contributor
Subject
Genre
Language
eng
Summary
This is the first volume of a collection of articles dedicated to V.G Maz'ya on the occasion of his 60th birthday. It contains surveys on his work in different fields of mathematics or on areas to which he made essential contributions. Other articles of this book have their origin in the common work with Maz'ya. V.G Maz'ya is author or co-author of more than 300 scientific works on various fields of functional analysis, function theory, numerical analysis, partial differential equations and their application. The reviews in this book show his enormous productivity and the large variety of his work. The scond volume contains most of the invited lectures of the Conference on Functional Analysis, Partial Differential Equations and Applications held in Rostock in September 1998 in honor of V.G Maz'ya. Here different problems of functional analysis, potential theory, linear and nonlinear partial differential equations, theory of function spaces and numerical analysis are treated. The authors, who are outstanding experts in these fields, present surveys as well as new results
Member of
Cataloging source
I9W
http://library.link/vocab/creatorName
Rossmann, Jürgen
Dewey number
510
Index
no index present
LC call number
QA1-939
Literary form
non fiction
Nature of contents
encyclopedias
http://library.link/vocab/relatedWorkOrContributorName
  • Takac, Peter
  • Wildenhain, Gunther
Series statement
Operator Theory: Advances and Applications
Series volume
109
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematics
Label
The Maz'ya Anniversary Collection : Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications, edited by Jürgen Rossmann, Peter Takáč, Günther Wildenhain, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-0348-8675-8
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Vladimir Maz'ya: Friend and mathematician. Recollections -- On Maz'ya's work in potential theory and the theory of function spaces -- 1. Introduction -- 2. Embeddings and isoperimetric inequalities -- 3. Regularity of solutions -- 4. Boundary regularity -- 5. Nonlinear potential theory -- Maz'ya's works in the linear theory of water waves -- 1. Introduction -- 2. The unique solvability of the water wave problem -- 3. The Neumann-Kelvin problem -- 4. Asymptotic expansions for transient water waves due to brief and high-frequency disturbances -- Maz'ya's work on integral and pseudodifferential operators -- 1. Non-elliptic operators -- 2. Oblique derivative problem: breakthrough in the generic case of degeneration -- 3. Estimates for differential operators in the half-space -- 4. The characteristic Cauchy problem for hyperbolic equations -- 5. New methods for solving ill-posed boundary value problems -- 6. Applications of multiplier theory to integral operators -- 7. Integral equations of harmonic potential theory on general non-regular surfaces -- 8. Boundary integral equations on piecewise smooth surfaces -- Contributions of V. Maz'ya to the theory of boundary value problems in nonsmooth domains -- 1. Maz'ya's early work on boundary value problems in nonsmooth domains -- 2. General elliptic boundary value problems in domains with point singularities -- 3. Boundary value problems in domains with edges -- 4. Spectral properties of operator pencils generated by elliptic boundary value problems in a cone -- 5. Applications to elastostatics and hydrodynamics -- 6. Singularities of solutions to nonlinear elliptic equations at a cone vertex -- On some potential theoretic themes in function theory -- 1. Approximation theory -- 2. Uniqueness properties of analytic functions -- 3. The Cauchy problem for the Laplace equation -- Approximate approximations and their applications -- 1. Introduction -- 2. Quasi-interpolation -- 3. Generating functions for quasi-interpolation of high order -- 4. Semi-analytic cubature formulas -- 5. Cubature of integral operators over bounded domains -- 6. Approximate wavelets -- 7. Numerical algorithms based upon approximate approximations -- Maz'ya's work on the biography of Hadamard -- Isoperimetric inequalities and capacities on Riemannian manifolds -- 1. Introduction -- 2. Capacity of balls -- 3. Parabolicity of manifolds -- 4. Isoperimetric inequality and Sobolev inequality -- 5. Capacity and the principal frequency -- 6. Cheeger's inequality -- 7. Eigenvalues of balls on spherically symmetric manifolds -- 8. Heat kernel on spherically symmetric manifolds -- Multipliers of differentiable functions and their traces -- 1. Introduction -- 2. Description and properties of multipliers -- 3. Multipliers in the space of Bessel potentials as traces of multipliers -- An asymptotic theory of nonlinear abstract higher order ordinary differential equations -- Sobolev spaces for domains with cusps -- 1. Introduction -- 2. Extension theorems -- 3. Embedding theorems -- 4. Boundary values of Sobolev functions -- Extension theorems for Sobolev spaces -- 1. Introduction -- 2. Extensions with preservation of class -- 3. Estimates for the minimal norm of an extension operator -- 4. Extensions with deterioration of class -- Contributions of V.G. Maz'ya to analysis of singularly perturbed boundary value problems -- 1. Introduction -- 2. Domain with a small hole -- 3. General asymptotic theory by Maz'ya, Nazarov and Plamenevskii -- 4. Asymptotics of solutions of boundary integral equations under a small perturbation of a corner -- 5. Compound asymptotics for homogenization problems -- 6. Boundary value problems in 3D-1D multi-structures -- Asymptotic analysis of a mixed boundary value problem in a singularly degenerating domain -- 1. Introduction -- 2. Formulation of the problem -- 3. The leading order approximation -- A history of the Cosserat spectrum -- 1. Introduction -- 2. The first boundary value problem of elastostatics -- 3. The second and other boundary-value problems -- 4. Applications and other related results -- Boundary integral equations for plane domains with cusps -- 1. Introduction -- 2. Integral equations in weighted Sobolev spaces -- On Maz'ya type inequalities for convolution operators -- 1. Introduction -- 2. One-dimensional polynomials -- 3. The functions ?x?2? in ? n -- Sharp constants and maximum principles for elliptic and parabolic systems with continuous boundary data -- 1. The norm and the essential norm of the double layer elastic and hydrodynamic potentials in the space of continuous functions -- 2. Exact constants in inequalities of maximum principle type for certain systems and equations of mathematical physics -- 3. Maximum modulus principle for elliptic systems -- 4. Maximum modulus principle for parabolic systems -- 5. Maximum norm principle for parabolic systems -- Lp-contractivity of semigroups generated by parabolic matrix differential operators -- 1. Introduction -- 2. Preliminaries -- 3. Weakly coupled systems -- 4. Coupled systems -- Curriculum vitae of Vladimir Maz'ya -- Publications of Vladimir Maz'ya
Dimensions
unknown
Extent
1 online resource (364 pages).
Form of item
online
Isbn
9783034886758
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-8675-8
Specific material designation
remote
System control number
  • (OCoLC)840290626
  • (OCoLC)ocn840290626
Label
The Maz'ya Anniversary Collection : Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications, edited by Jürgen Rossmann, Peter Takáč, Günther Wildenhain, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-0348-8675-8
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Vladimir Maz'ya: Friend and mathematician. Recollections -- On Maz'ya's work in potential theory and the theory of function spaces -- 1. Introduction -- 2. Embeddings and isoperimetric inequalities -- 3. Regularity of solutions -- 4. Boundary regularity -- 5. Nonlinear potential theory -- Maz'ya's works in the linear theory of water waves -- 1. Introduction -- 2. The unique solvability of the water wave problem -- 3. The Neumann-Kelvin problem -- 4. Asymptotic expansions for transient water waves due to brief and high-frequency disturbances -- Maz'ya's work on integral and pseudodifferential operators -- 1. Non-elliptic operators -- 2. Oblique derivative problem: breakthrough in the generic case of degeneration -- 3. Estimates for differential operators in the half-space -- 4. The characteristic Cauchy problem for hyperbolic equations -- 5. New methods for solving ill-posed boundary value problems -- 6. Applications of multiplier theory to integral operators -- 7. Integral equations of harmonic potential theory on general non-regular surfaces -- 8. Boundary integral equations on piecewise smooth surfaces -- Contributions of V. Maz'ya to the theory of boundary value problems in nonsmooth domains -- 1. Maz'ya's early work on boundary value problems in nonsmooth domains -- 2. General elliptic boundary value problems in domains with point singularities -- 3. Boundary value problems in domains with edges -- 4. Spectral properties of operator pencils generated by elliptic boundary value problems in a cone -- 5. Applications to elastostatics and hydrodynamics -- 6. Singularities of solutions to nonlinear elliptic equations at a cone vertex -- On some potential theoretic themes in function theory -- 1. Approximation theory -- 2. Uniqueness properties of analytic functions -- 3. The Cauchy problem for the Laplace equation -- Approximate approximations and their applications -- 1. Introduction -- 2. Quasi-interpolation -- 3. Generating functions for quasi-interpolation of high order -- 4. Semi-analytic cubature formulas -- 5. Cubature of integral operators over bounded domains -- 6. Approximate wavelets -- 7. Numerical algorithms based upon approximate approximations -- Maz'ya's work on the biography of Hadamard -- Isoperimetric inequalities and capacities on Riemannian manifolds -- 1. Introduction -- 2. Capacity of balls -- 3. Parabolicity of manifolds -- 4. Isoperimetric inequality and Sobolev inequality -- 5. Capacity and the principal frequency -- 6. Cheeger's inequality -- 7. Eigenvalues of balls on spherically symmetric manifolds -- 8. Heat kernel on spherically symmetric manifolds -- Multipliers of differentiable functions and their traces -- 1. Introduction -- 2. Description and properties of multipliers -- 3. Multipliers in the space of Bessel potentials as traces of multipliers -- An asymptotic theory of nonlinear abstract higher order ordinary differential equations -- Sobolev spaces for domains with cusps -- 1. Introduction -- 2. Extension theorems -- 3. Embedding theorems -- 4. Boundary values of Sobolev functions -- Extension theorems for Sobolev spaces -- 1. Introduction -- 2. Extensions with preservation of class -- 3. Estimates for the minimal norm of an extension operator -- 4. Extensions with deterioration of class -- Contributions of V.G. Maz'ya to analysis of singularly perturbed boundary value problems -- 1. Introduction -- 2. Domain with a small hole -- 3. General asymptotic theory by Maz'ya, Nazarov and Plamenevskii -- 4. Asymptotics of solutions of boundary integral equations under a small perturbation of a corner -- 5. Compound asymptotics for homogenization problems -- 6. Boundary value problems in 3D-1D multi-structures -- Asymptotic analysis of a mixed boundary value problem in a singularly degenerating domain -- 1. Introduction -- 2. Formulation of the problem -- 3. The leading order approximation -- A history of the Cosserat spectrum -- 1. Introduction -- 2. The first boundary value problem of elastostatics -- 3. The second and other boundary-value problems -- 4. Applications and other related results -- Boundary integral equations for plane domains with cusps -- 1. Introduction -- 2. Integral equations in weighted Sobolev spaces -- On Maz'ya type inequalities for convolution operators -- 1. Introduction -- 2. One-dimensional polynomials -- 3. The functions ?x?2? in ? n -- Sharp constants and maximum principles for elliptic and parabolic systems with continuous boundary data -- 1. The norm and the essential norm of the double layer elastic and hydrodynamic potentials in the space of continuous functions -- 2. Exact constants in inequalities of maximum principle type for certain systems and equations of mathematical physics -- 3. Maximum modulus principle for elliptic systems -- 4. Maximum modulus principle for parabolic systems -- 5. Maximum norm principle for parabolic systems -- Lp-contractivity of semigroups generated by parabolic matrix differential operators -- 1. Introduction -- 2. Preliminaries -- 3. Weakly coupled systems -- 4. Coupled systems -- Curriculum vitae of Vladimir Maz'ya -- Publications of Vladimir Maz'ya
Dimensions
unknown
Extent
1 online resource (364 pages).
Form of item
online
Isbn
9783034886758
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-8675-8
Specific material designation
remote
System control number
  • (OCoLC)840290626
  • (OCoLC)ocn840290626

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