Nazarov S., Plamenevsky B.A. Elliptic Problems in Domains with Piecewise Smooth Boundaries

Berlin: de Gruyter, 1994. — 536 p.Introduction
Elliptic boundary value problems in domains with smooth boundary
Elliptic boundary value problems
Elliptic problems with a parameter
Dirichlet and Neumann problems for the Laplace operator in plane domains with corner points at the boundary
Generalized solutions of the Dirichlet and Neumann problems in domains with corner points. Deviations from the "usual" properties of solutions
Solvability and asymptotics of solutions of model problems in a strip and in an angle
The Dirichlet problem in a bounded domain with a corner point
The Neumann problem in a bounded domain with a corner point
General elliptic boundary value problems in a cylinder and in a cone
Solvability and asymptotics of solutions of boundary value problems in a cylinder with the coefficients constant along the axis
Calculation of the coefficients cv(k,j) in the asymptotics of the solution
Asymptotics of the solutions of boundary value problems in a cylinder with right-hand side of a special form
Solvability and asymptotics of solutions of the boundary value problems with periodic coefficients
Boundary value problems in a cone
Estimates and asymptotics of solutions in Lp and Holder classes
Fundamental solutions of the boundary value problem in a cone
Two examples: The Dirichlet problem and the oblique derivative problem
General elliptic problems in domains with conical points
The Fredholm property
Asymptotics of solutions near conical points
Expressions for the coefficients in asymptotic formulas. Properties of the index
Asymptotics of fundamental solutions
Boundary value problems in spaces with nonhomogeneous norms
Self-adjoint problems in domains with outlets to infinity
Self-adjoint problems in domains with cylindrical outlets to infinity
Special choices of Jordan chains of self-adjoint operator pencils
Waves, scattering matrices and intrinsic radiation conditions
Energetic solutions and the polarization matrix
The extensions of the symmetric operator
On a problem of the scattering of electro-magnetic waves
Elasticity problems in domains having cylindrical outlets to infinity
Stokes and Navier-Stokes problems in domains with cylindrical outlets to infinity
Self-adjoint problems in domains with conical points. Applications
Self-adjoint problems. Properties of their pencils
The generalized Green formula, radiation conditions
Self-adjoint extensions in spaces with weighted norms
Boundary value problems in domains with compact complement. The polarization matrix
Asymptotic analysis of the problem in domains with small holes
Two problems in plates theory
Applications to crack theory
Stress singularities at a crack tip
The rupture criterion
The Cherepanov-Rice integral
On the structure of the spectrum of the pencil generated by a self-adjoint problem in a plane domain with a crack
Elliptic problems in domains with smooth edges
Statement of the problem. Model problems
Analysis of the model problems
The Fredholm property of the elliptic problem in a bounded domain
The Dirichlet and the Neumann problems for self-adjoint systems
Lp-estimates of solutions
Estimates of solutions in weighted Holder classes
Elliptic problems on manifolds with intersecting edges
Manifolds of the class D
Differential operators on class D manifolds
The function spaces
Statement of the boundary problems. Model problems
Boundary value problems on class D manifolds
The Dirichlet and Neumann problems for self-adjoint systems
Asymptotics of solutions of the Dirichlet problem for the Laplace operator in a three-dimensional domain having edges on the boundary
Asymptotics of solution near smooth edges
Asymptotics of solutions near the singular point having the type of the vertex of a polyhedron
Formulas for coefficients in asymptotics of solutions near an edge
The asymptotics of solutions of general problems near edges
Guidelines for constructing asymptotics. Auxiliary assertions
The asymptotics of solutions near an edge (in case of a smooth right-hand side)
Asymptotics of solutions near an edge (general case)
Corollaries of asymptotic formulas
Self-adjoint problems with radiation conditions on the edges
Setting of boundary value problems and information about the asymptotics of solutions
The generalized Green formula. Fredholm property of the problem with radiation conditions
Solvability conditions for the problem with radiation conditions in terms of the generalized Green formula
Intrinsic radiation conditions on the edge
Energetic radiation conditions. The polarization operator on the edge
The scattering operator. The formula for the increment of the dimension of the kernel of the operator of the problem generated by the variation of the weight factor
Sobolev problems
The three-dimensional problem of crack mechanics
Bibliographical notes
References
Index
List of spaces