Implicit Partial Differential Equations: v. 37 (Progress in Nonlinear Differential Equations and Their Applications) - Hardcover

Dacorogna, Bernard; Marcellini, Paolo

9783764341213: Implicit Partial Differential Equations: v. 37 (Progress in Nonlinear Differential Equations and Their Applications)

Hardcover

ISBN 10: 3764341211 ISBN 13: 9783764341213

Publisher: Birkhauser Verlag AG, 1999

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This text presents a functional analytic method for handling a large class of nonlinear partial differential equations and systems. Results obtained by this method have important applications to the calculus of variations, nonlinear elasticity, problems of phase transitions and optimal design.

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Review

"Provides a self-contained development of the new kind of differential equations... Includes many examples helpful in understanding the theory and is well [and] clearly written."

―Mathematical Reviews

"...Topics of the book have important applications in variational calculus, nonlinear elasticity, phase transitions, and optimal design. In particular, Part IV (Chapters 7-9) includes the singular value case, the case of potential wells, and the complex eikonal equation. A lot of background material, as viscosity solutions, quasiconvexity and related topics, piecewise polynomial approximation in Sobolev spaces, convex integration, or nonclassical Vitali-type covering theorems, is presented in the book, which makes it essentially self-contained. Most of the results are original from the authors, some results are published even first time. This makes the book a unique introduction to this new topic, and will be found useful by experts in nonlinear analysis in general and PDEs in particular, as well as by advanced graduate students in this field."

–Zentralblatt Math

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