Title | The Maz'ya Anniversary Collection [electronic resource] : Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications / edited by Jรผrgen Rossmann, Peter Takรกฤ, Gรผnther Wildenhain |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1999 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8675-8 |
Descript | XII, 364 p. online resource |
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