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The Maz’ya Anniversary Collection Volume 1: On Maz’ya’s work in functional analysis, partial differential equations and applications

The contributions in this volume are dedicated to Vladimir G. Maz'ya and are par­ tially based on talks given at the conference "Functional Analysis, Partial Differ­ ential Equations, and Applications", which took place at the University of Rostock from August 31 to September 4, 1998,...

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Bibliographic Details
Other Authors: Rossmann, Jürgen (Editor), Takac, Peter (Editor), Wildenhain, Günther (Editor)
Format: eBook
Language:English
Published: Basel Birkhäuser 1999, 1999
Edition:1st ed. 1999
Series:Operator Theory: Advances and Applications
Subjects:
Mathematical Analysis
Analysis
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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 Cauchyproblem for the Laplace equation
  • Approximate approximations and their applications
  • 1. Introduction
  • 2. Quasi-interpolation
  • 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
  • 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 homogenizationproblems
  • 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
  • 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
  • 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

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