This monograph presents extensions of the Moser-Bangert approach that include solutions of a family of nonlinear elliptic PDEs on
R
n
and an Allen-Cahn PDE model of phase transitions.
After recalling the relevant Moser-Bangert results,
Extensions of Moser-Bangert Theory
pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties. Subsequent chapters build upon the introductory results, making the monograph self contained.
The work is intended for mathematicians who specialize in partial differential equations and may also be used as a text for a graduate topics course in PDEs.
Rezensionen / Stimmen
From the reviews:
"This book contains a study of the solution set to (PDE), expanding work by Moser and Bangert and previous work by the authors for (AC). . This is an important piece of work concerning a difficult and deep matter. . This a very good demonstration of the power of variational methods, showing that they can be modified, extended and combined in order to deal with many different kinds of problems." (Jesús Hernández, Mathematical Reviews, Issue 2012 m)
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ISBN-13
978-0-8176-8117-3 (9780817681173)
DOI
10.1007/978-0-8176-8117-3
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