Translations of Mathematical Monographs 1983; 522 pp; hardcover Volume: 57 ISBN10: 0821845101 ISBN13: 9780821845103 List Price: US$135 Member Price: US$108 Order Code: MMONO/57
 This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundaryvalue problems with free boundaries. The first part has to do with the general theory of boundaryvalue problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundaryvalue problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elasticoplasticity. Table of Contents Part I Boundaryvalue problems in the theory of analytic functions and their application to hydrodynamics  I. The boundaryvalue problems of Riemann and Hilbert
 II. Singular operators in spaces of summable functions. Application to boundaryvalue problems and to the study of boundary properties of analytic functions
 III. The mixed boundaryvalue problem with free boundary
 IV. Flows of an incompressible fluid with free boundaries
Part II Generalized solutions of quasilinear systems of equations in the mechanics of continuous media  V. Quasiconformal mappings and generalized solutions of elliptic systems of equations on the plane
 VI. Boundaryvalue problems
 VII. Boundaryvalue problems in hydrodynamics and subsonic gas dynamics
 VIII. Problems in filtration theory for a fluid with free boundaries
 IX. Some planar problems with an unknown boundary in elasticity theory
