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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 o...
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