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The book collects many techniques that are helpul in obtaining regularity results for solutions of nonlinear systems of partial differential equations. They are then applied in various cases to provide useful examples and relevant results, particularly in fields like fluid mechanics, solid mechanics, semiconductor theory, or game theory.
In general, these techniques are scattered in the journal literature and developed in the strict context of a given model. In the book, they are presented independently of specific models, so that the main ideas are explained, while remaining applicable to various situations. Such a presentation will facilitate application and implementation by researchers, as well as teaching to students.
List of contents
General Technical Results.- General Regularity Results.- Nonlinear Elliptic Systems Arising from Stochastic Games.- Nonlinear Elliptic Systems Arising from Ergodic Control.- Harmonic Mappings.- Nonlinear Elliptic Systems Arising from the Theory of Semiconductors.- Stationary Navier-Stokes Equations.- Strongly Coupled Elliptic Systems.- Dual Approach to Nonlinear Elliptic Systems.- Nonlinear Elliptic Systems Arising from plasticity Theory.
Summary
The book contains many techniques that are helpful in obtaining regularity results for solutions of nonlinear systems of partial differential equations. They are then applied in various cases to provide useful examples and relevant results, particularly in fields such as fluid mechanics, solid mechanics, semiconductor theory, and game theory.
Additional text
From the reviews:
"The book under review presents several topics of the regularity theory for nonlinear elliptic equations and systems which have been developed in recent years. … It may serve for teaching to higher graduate students and for researchers in the field of nonlinear PDE’s." (Joachim Naumann, Zentralblatt MATH, Vol. 1055, 2005)
"It is a pleasure to review this new book by Bensoussan and Frehse; indeed this work covers remarkable, finely selected, updated material … . this book is a very interesting and useful source of material for those interested in the latest developments of regularity theory of solutions of nonlinear elliptic systems. … the book is an essential companion to the standard monographs already available and it is bound to become a standard and inevitable item in any list of references on the subject." (Giuseppe Mingione, Mathematical Reviews, 2004 a)
Report
From the reviews:
"The book under review presents several topics of the regularity theory for nonlinear elliptic equations and systems which have been developed in recent years. ... It may serve for teaching to higher graduate students and for researchers in the field of nonlinear PDE's." (Joachim Naumann, Zentralblatt MATH, Vol. 1055, 2005)
"It is a pleasure to review this new book by Bensoussan and Frehse; indeed this work covers remarkable, finely selected, updated material ... . this book is a very interesting and useful source of material for those interested in the latest developments of regularity theory of solutions of nonlinear elliptic systems. ... the book is an essential companion to the standard monographs already available and it is bound to become a standard and inevitable item in any list of references on the subject." (Giuseppe Mingione, Mathematical Reviews, 2004 a)
