Generalized Young Measures and Calculus of Variations

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Tavakoli, Alireza | 2020

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52662 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi Firouzabad, Morteza
Abstract:
In this thesis, issues related to the minimization of a class of energy functions defined over the space of vector valued functions, under a linear differential constraint are discussed. We collect a series of lower semi-continuity results with respect to the weak convergence obtained by using the tools of Young measures int the case of growth condition larger than one and using generalized Young measures in linear growth case.The general trend in these results is to obtain a good representation of the energy limit by a quantitative study of the oscillation and concentration effects in a weakly convergent sequence
Keywords:
Variation Calculus ; Quasi Convexity ; Young Measures