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,...
Other Authors: | , , |
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Format: | eBook |
Language: | English |
Published: |
Basel
Birkhäuser
1999, 1999
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Edition: | 1st ed. 1999 |
Series: | Operator Theory: Advances and Applications
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Subjects: | |
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