Eugene Shargorodsky's Books

Bernoulli Free-Boundary Problems

By: Eugene Shargorodsky,John F. Toland

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Bernoulli Free-Boundary Problems

By: Eugene Shargorodsky,John F. Toland

Questions of existence, multiplicity, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems. In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable.

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Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821841890

ISBN 13

9780821841891

Decision Making in Otolaryngology

By: Cuneyt Alper,Eugene Myers,David Eibling

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Decision Making in Otolaryngology

By: Cuneyt Alper,Eugene Myers,David Eibling

The new edition of this algorithm-based resource provides clinicians and trainees with the latest advances in the evaluation and management of otolaryngologic disorders. Divided into seven sections, the book discusses numerous problems in each part of the ENT system, presenting up to date basic science and surgical techniques. Each chapter follows a logical, step by step approach covering both common and less common conditions. The second edition has been fully revised and includes 36 new chapters with a number of them focusing on paediatric disorders. Authored by an internationally recognised team of Pittsburgh-based experts, this book is enhanced by images and diagrams to assist learning. Key Points Fully revised, second edition providing latest advances in diagnosis and management of otolaryngologic disorders Covers both common and less common problems in all areas of the ENT system Includes 36 new chapters, many with focus on paediatric conditions Previous edition (9780721689654) published in 2001

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440

Publisher

Jaypee Brothers Medical Publishers

Published Date

ISBN 10

9386056089

ISBN 13

9789386056085

Bernoulli Free-boundary Problems

By: Eugene Shargorodsky,John F. Toland

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Bernoulli Free-boundary Problems

By: Eugene Shargorodsky,John F. Toland

When a domain in the plane is specified by the requirement that there exists a harmonic function which is zero on its boundary and additionally satisfies a prescribed Neumann condition there, the boundary is called a Bernoulli free boundary. (The boundary is 'free' because the domain is not known a priori and the name Bernoulli was originally associated with such problems in hydrodynamics.) Questions of existence, multiplicity or uniqueness, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems.In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable. The authors impose no restriction on the amplitudes or shapes of free boundaries, nor on their smoothness. Therefore the equivalence is global, and valid even for very weak solutions. An essential observation here is that the equivalent equations can be written as nonlinear Riemann-Hilbert problems and the theory of complex Hardy spaces in the unit disc has a central role. An additional useful fact is that they have gradient structure, their solutions being critical points of a natural Lagrangian. This means that a canonical Morse index can be assigned to free boundaries and the Calculus of Variations becomes available as a tool for the study. Some rather natural conjectures about the regularity of free boundaries remain unresolved.

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Publisher

American Mathematical Soc.

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ISBN 10

1470405202

ISBN 13

9781470405205

Book's by Eugene Shargorodsky

Bernoulli Free-Boundary Problems

Bernoulli Free-Boundary Problems

Decision Making in Otolaryngology

Decision Making in Otolaryngology

Bernoulli Free-boundary Problems

Bernoulli Free-boundary Problems

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