S.L. Sobolev (1908–1989) was a great mathematician of the twentieth century. His selected works included in this volume laid the foundations for intensive development of the modern theory of partial differential equations and equations of mathematical physics, and they were a gold mine for new directions of functional analysis and computational mathematics.

The topics covered in this volume include Sobolev’s fundamental works on equations of mathematical physics, computational mathematics, and cubature formulas. Some of the articles are generally unknown to mathematicians because they were published in journals that are difficult to access.

Springer US; December 2006

628 pages; ISBN 9780387341491

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Title:

Selected Works of S.L. Sobolev
Author: Gennadii V. Demidenko; Vladimir Vaskevich

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 Equation 20. Optimal Mechanical Cubature Formulas with Nodes on a Regular Lattice 21. Constructing Cubature Formulas with Regular Boundary Layer 22. Convergence of Cubature Formulas on Infinitely Differentiable Functions 23. Convergence of Cubature Formulas on the Elements of L2^(m) 24. The Coefficients of Optimal Quadrature Formulas 25. On the Roots of Euler Polynomials 26. On the End Roots of Euler Polynomials 27. On the Asymptotics of the Roots of the Euler Polynomials 28. More on the Zeros of Euler Polynomials 29. On the Algebraic Order of Exactness of Formulas of Approximate Integration Index