Minimization of asymptotic energy of Müller's functional endowed with local nonlinear lower-order term

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• 作者：Andrija Raguž
• 刊名：PAMM
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：16
• 期：1
• 页码：661-662
• 全文大小：235K
• ISSN：1617-7061

文摘

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. (