Contents

Introduction 1

Part 1. Elliptic boundary value problems in domains with smooth

boundary 7

Chapter 1. Boundary value problems for ordinary differential equations on

the half-axis 9

1.1. The boundary value problem and its formally adjoint 9

1.2. Solvability of the boundary value problem on the half-axis 13

1.3. Solvability of regular problems on the half-axis in Sobolev spaces of

negative order 20

1.4. Properties of the operator adjoint to the operator of the boundary

value problem 26

Chapter 2. Elliptic boundary value problems in the half-space 31

2.1. Periodic solutions of partial differential equations 31

2.2. Solvability of elliptic boundary value problems in the half-space 35

2.3. Solvability of elliptic boundary value problems in the half-space in

Sobolev spaces of arbitrary integer order 43

Chapter 3. Elliptic boundary value problems in smooth domains 59

3.1. The boundary value problem and its formally adjoint 59

3.2. An a priori estimate for the solution 72

3.3. The adjoint operator 80

3.4. Solvability of elliptic boundary value problems in smooth domains 84

3.5. The Green function of the boundary value problem 90

3.6. Elliptic boundary value problems with parameter 98

Chapter 4. Variants and extensions 105

4.1. Elliptic problems with boundary operators of higher order in a smooth

bounded domain 105

4.2. Boundary value problems for elliptic systems of differential equations 111

4.3. Boundary value problems in the variational form 119

4.4. Further results 134

4.5. Notes 138

Part 2. Elliptic problems in domains with conical points 143

Chapter 5. Elliptic boundary value problems in an infinite cylinder 145