Selected Works of S. L. Sobolev: Vol.1 Selected Works of S.L. Sobolev

Preface Academician S. L. Sobolev is a Founder of New Directions of Functional Analysis (by Yu. G. Reshetnyak) Part I. Equations of Mathematical Physics 1. Application of the Theory of Plane Waves to the Lamb Problem 2. On a New Method in the Plane Problem on Elastic Vibrations 3. On Application of a New Method to Study Elastic Vibrations in a Space with Axial Symmetry 4. On Vibrations of a Half-Plane and a Layer with Arbitrary Initial Conditions 5. On a New Method of Solving Problems about Propagation of Vibrations 6. Functionally Invariant Solutions of the Wave Equation 7. General Theory of Diffraction of Waves on Riemann Surfaces 8. The Problem of Propagation of a Plastic State 9. On a New Problem of Mathematical Physics 10. On Motion of a Symmetric Top with a Cavity Filled with Fluid 11. On a Class of Problems of Mathematical Physics Part II. Computational Mathematics and Cubature Formulas 1. Schwarz's Algorithm in Elasticity Theory 2. On Solution Uniqueness of Difference Equations of Elliptic Type 3. On One Difference Equation 4. Certain Comments on the Numeric Solutions of Integral Equations 5. Certain Modern Questions of Computational Mathematics 6. Functional Analysis and Computational Mathematics 7. Formulas of Mechanical Cubatures in n-Dimensional Space 8. On Interpolation of Functions of n Variables 9. Various Types of Convergence of Cubature and Quadrature Formulas 10. Cubature Formulas on the Sphere Invariant under Finite Groups of Rotations 11. The Number of Nodes in Cubature Formulas on the Sphere 12. Certain Questions of the Theory of Cubature Formulas 13. A Method for Calculating theCoefficients in Mechanical Cubature Formulas 14. On the Rate of Convergence of Cubature Formulas 15. Theory of Cubature Formulas 16. Convergence of Approximate Integration Formulas for Functions from L2^(m) 17. Evaluation of Integrals of Infinitely Differentiable Functions 18. Cubature Formulas with Regular Boundary Layer 19. A Difference Analogue of the Polyharmonic