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Boundary value problems for second order elliptic equations
Applied Mathematics and Mechanics, Volume 5: Boundary Value Problems: For Second Order Elliptic Equations is a revised and augmented version of a lecture course on non-Fredholm elliptic boundary value problems, delivered at the Novosibirsk State University in the academic year 1964-1965. This seven-...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Amsterdam,
North-Holland Pub. Co.,
1968.
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| Colección: | North-Holland series in applied mathematics and mechanics ;
v. 5. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; Boundary Value Problems: For Second Order Elliptic Equations; Copyright Page; Preface; Table of Contents; Chapter I. INTRODUCTORY REMARKS; 1. Some definitions and notations; 2. General information on second order elliptic equations and boundary value problems; 3. Fundamental aspects of the theory of linear equations in normed linear spaces; 4. Fredholm integral equations of the second kind; 5. Singular integral equations; 6. Fredholm integral equations of the first kind; 7. Conventional classification of boundary value problems
- Chapter II. CERTAIN QUALITATIVE AND CONSTRUCTIVE PROPERTIES OF THE SOLUTIONS OF ELLIPTIC EQUATIONS1. The extremum principle; 2. The Hopf principle; 3. The Zaremba-Giraud principle; 4. The extremum principle for a class of elliptic systems; 5. Adjoint operators. Green's formula; 6. Existence of solutions; 7. Elementary solutions; 8. The principle elementary solution; 9. Generalised potentials and their properties; 10. General representation of the solutions of a class of elliptic systems; 11. Harmonic potentials of a simple and double layer and integrals of Cauchy type
- Chapter III. THE DIRICHLET PROBLEM FOR A SECOND ORDER ELLIPTIC EQUATION1. Formulation of the problem. Uniqueness of the solution.; 2. Existence of a solution of the problem (2.1), (3.1); 3. The Dirichlet problem for the Laplace equation in two independent variables. Green's function; 4. The Riemann-Hilbert problem and integral representations of holomorphic functions; Chapter IV. THE DIRICHLET PROBLEM FOR ELLIPTIC SYSTEMS; 1. Preliminary remarks; 2. Uniqueness of the solution of the Dirichlet problem; 3. Elliptic systems (4.1) with the principal part in the form of the Laplace operator
- 4. The Dirichlet problem for the elliptic system (4.11) with analytic coefficients5. The Dirichlet problem for system (4.1); 6. General representation of the solutions of system (4.71); 7. The Dirichlet problem for a weakly connected system (4.71); 8. Some remarks concerning strongly connected systems; 9. The Dirichlet problem for system (4.96); 10. Influencing effect of coefficients of the smaller derivatives .; Chapter V. THE DIRECTIONAL DERIVATIVE PROBLEM FOR EQUATION (2.1) WHEN THE DIRECTION OF INCLINATION IS NOT TANGENTIAL TO THE BOUNDARY; 1. Formulation of the problem
- 2. Investigation of the Neumann problem3. The adjoint problem; 4. Investigation of the directional derivative problem (5.1), (5.2) when condition (5.4) is satisfied; Chapter VI. THE POINCAR�E PROBLEM FOR SECOND ORDER ELLIPTIC SYSTEMS IN TWO INDEPENDENT VARIABLES; 1. General remarks; 2. The Poincar�e problem for system (4.18) with analytic coefficients; 3. Certain special cases of the problem (4.18), (6.1); 4. The Poincar�e problem for the uniformly elliptic system (4.1).; 5. The Poincar�e problem for elliptic systems (4.71) with constant coefficients