Minimization of asymptotic energy of Müller's functional endowed with local nonlinear lower‐order term
Andrija Raguž · PAMM · 2016
Abstract We solve a minimization problem associated to a generalization of the Müller functional studied in the paper G. Alberti, S. Müller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761–825 (2001), whereby the lower order term ∫10a(s)v2(s)ds (involving a primitive of the mass density function, v = v(s), and the weight function a = a(s)) is replaced by ∫10a(s, v(s), v′(s))v2(s)ds (where a belongs to a suitable Carathéodory class). We calculate the rescaled asymptotic energy of the functional as small parameter epsilon tends to zero. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)