Effect of a Singular Perturbation to a 1-d Non-Convex Variational Problem

By (author) Markus Lilli

Extent: 100, 100 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Series: Augsburger Schriften zur Mathematik, Physik und Informatik

Series volume number: 10

Language: English

(Paperback) (Published)

(November 2005)

ISBN: 9783832509286

5.71 x 8.27 inches

Price: $61.00

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Synopsis
Contributing Authors

Nonconvex variational problems are of importance in modeling problems of microstructures and elasticity. In this book, we consider a $1$-d nonconvex problem and we prove existence of solutions of the corresponding non-elliptic Euler-Lagrange equation by considering the Euler-Lagrange equation of the singular perturbed variational problem and passing to the limit. Under general assumptions on the potential we prove existence of Young-measure solutions. More restrictive conditions on the potential yield classical solutions via a topological method. The singular perturbed problem, which is also of interest for physicists due to the higher gradient surface-energy, is discussed in big detail.

By (author) Markus Lilli

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Effect of a Singular Perturbation to a 1-d Non-Convex Variational Problem

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