The Effect of a Singular Perturbation to a 1-D Non-Convex Variational Problem (Paperback) (ISBN-13: 9783832509286)

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.

Author: Markus LILLI
ISBN-10: 3832509283
ISBN-13: 9783832509286
Publisher: Logos Verlag Berlin
Language: English
Published: 11/15/2005
Pages: 100
Format: Paperback