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Boundary-Value Problems with Free Boundaries for Elliptic Systems of Equations
V. N. Monakhov

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
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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.

Table of Contents

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
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