Hardcover ISBN:  9780821845103 
Product Code:  MMONO/57 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Electronic ISBN:  9781470444716 
Product Code:  MMONO/57.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 

Book DetailsTranslations of Mathematical MonographsVolume: 57; 1983; 522 ppMSC: Primary 35; Secondary 30;
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


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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.

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