Preface. 0. Introduction. 1. Functional Spaces. 2. Space Hs,p,(r)(Omega) 3. Elliptic Boundary-Value Problem. 4. Theorem on Complete Collection of Isomorphisms. 5. Elliptic Problems with Normal Boundary Conditions. 6. Traces of Generalized Solutions of Elliptic Equations on the Boundary of the Domain. 7. Local Increase in the Smoothness of Generalized Solutions of Elliptic Boundary-Value Problems, Green's Functions. 8. Elliptic Problems with Power Singularities on the Right-Hand Sides. Degenerate Elliptic Problems. 9. Elliptic Boundary-Value Problems with a Parameter. 10. Elliptic Boundary-Value Problems for Systems of Equations. Bibliographical Notes. References. Subject Index. Notation.
`The book is well written and deals well with a topic which requires great care and attention to detail. It is an excellent digest of known results for this problem and a valuable reference for those who wish to apply known results for problem (1) to various other disciplines.
' SIAM Review, 40:1 (1998)
(2) Green's functions were constructed and studied for general elliptic boundary-va lue problems ([BeRI]-[Ber3], [Kovl], and [Kov2]). (3) Generalized eigenfunctions, spectral function, etc., were investigated in spectral theory [Ber]. (4) Elliptic boundary-value problems with arbitrary power singularities on the right hand sides were investigated ([Roi6], [Kos2,] and [Ser)). (5) A family of elliptic problems was studied in a family of expanding domains; the obtained results were applied to the investigation of elliptic problems with time deriva tives in the boundary conditions and parabolic problems in noncylindrical domains ([Kre3], [KLa], and [IKK)). (6) Strongly degenerate elliptic problems were studied in [RShI5]-[RShI8]. (7) Application to the investigation of traces of generalized solutions of equations on the boundary of the domain ([Roi8], [Roi4], [Roil5], and [RoiI7D. (8) Application to problems of transmission ([Roi3], [Roi4], [RSh6], and [RShlOD. (9) Applications to the investigation of nonlocal elliptic problems ([RSh7]-[RSh9], [RShll], and [RShI2)). (10) Application to problems of optimal control ([Li05], [RSh13], and [RShI4D. (11) Application to the theory of underdetermined and overdetermined problems ([Klvl]-[KLv3D. (12) Application to nonlinear problems ([Lio6] and [KrSD. (13) Application to the problems of mechanical motion of non-Newton liquids [Lit]. These and many other examples demonstrate that the efforts of the reader who wants to become an expert in the theory developed in the book will give fruitful results very quickly.
0. Introduction.- 1. Functional Spaces.- 2. Space $$tilde H^{s,p(r)} left( Omega right)$$.- 3. Elliptic Boundary-Value Problem.- 4. Theorem on Complete Collection of Isomorphisms.- 5. Elliptic Problems with Normal Boundary Conditions.- 6. Traces of Generalized Solutions of Elliptic Equations on the Boundary of the Domain.- 7. Local Increase in the Smoothness of Generalized Solutions of Elliptic Boundary-Value Problems. Green's Functions.- 8. Elliptic Problems with Power Singularities on the Right-Hand Sides. Degenerate Elliptic Problems.- 9. Elliptic Boundary-Value Problems with a Parameter.- 10. Elliptic Boundary-Value Problems for Systems of Equations.- Bibliographical Notes.- References.- Notation.
`The book is well written and deals well with a topic which requires great care and attention to detail. It is an excellent digest of known results for this problem and a valuable reference for those who wish to apply known results for problem (1) to various other disciplines.
' SIAM Review, 40:1 (1998)
Springer Book Archives
