Regularity Results for Nonlinear Elliptic Systems and Applications [Hardcover]

This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.

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 NavierStokes Equations.- Strongly Coupled Elliptic Systems.- Dual Approach to Nonlinear Elliptic Systems.- Nonlinear Elliptic Systems Arising from plasticity Theory.

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 PDEs. (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)

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, pal“;