文档介绍：Contents
Introduction 1
Part 1. Singularities of solutions to equations of mathematical
physics 7
Chapter 1. Prerequisites on operator pencils 9
. Operator pencils 10
. Operator pencils corresponding to sesquilinear forms 15
. A variational principle for operator pencils 21
. Elliptic boundary value problems in domains with conic points: some
basic results 26
. Notes 31
Chapter 2. Angle and conic singularities of harmonic functions 35
. Boundary value problems for the Laplace operator in an angle 36
. The Dirichlet problem for the Laplace operator in a cone 40
. The Neumann problem for the Laplace operator in a cone 45
. The problem with oblique derivative 49
. Further results 52
. Applications to boundary value problems for the Laplace equation 54
. Notes 57
Chapter 3. The Dirichlet problem for the Lam´esystem 61
. The Dirichlet problem for the Lam´esystem in a plane angle 64
. The operator pencil generated by the Dirichlet problem in a cone 74
. Properties of real eigenvalues 83
. The set functions Γ and Fν 88
. A variational principle for real eigenvalues 91
. Estimates for the width of the energy strip 93
. Eigenvalues for circular cones 97
. Applications 100
. Notes 105
Chapter 4. Other boundary value problems for the Lam´esystem 107
. A mixed boundary value problem for the Lam´esystem 108
. The Neumann problem for the Lam´esystem in a plane angle 120
. The Neumann problem for the Lam´esystem in a cone 125
. Angular crack in an anisotropic elastic space 133
. Notes 138
Chapter 5. The Dirichlet problem for the Stokes system 139
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. The Dirichlet problem for the Stokes system in an angle 142
. The operator pencil generated by the Dirichlet problem in a cone 148
. Properties of real eigenvalues 155
. The eigenvalues λ=1 and λ=–2 159
. A variational principle for real eigenvalues 168
5.