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Boundary-Value Problems with Free Boundaries for Elliptic Systems of Equations
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Translations of Mathematical Monographs
1983; 522 pp; hardcover
Volume: 57
ISBN-10: 0-8218-4510-1
ISBN-13: 978-0-8218-4510-3
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: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value 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 elastico-plasticity.

Part I Boundary-value problems in the theory of analytic functions and their application to hydrodynamics
• I. The boundary-value problems of Riemann and Hilbert
• II. Singular operators in spaces of summable functions. Application to boundary-value problems and to the study of boundary properties of analytic functions
• III. The mixed boundary-value 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. Boundary-value problems
• VII. Boundary-value 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