Minimization problems involving polyconvex integrands

Relaxation;Duality;Lack of compactness;Euler-lagrange equations and polar factorization

Awi, Romeo Olivier ; Gangbo, Wilfrid Mathematics de la Llave, Rafael Loss, Michael Swiech, Andrzej Yavari, Arash ; Gangbo, Wilfrid

University:Georgia Institute of Technology

Department:Mathematics

关键词: Relaxation;    Duality;    Lack of compactness;    Euler-lagrange equations and polar factorization;   

Others  :  https://smartech.gatech.edu/bitstream/1853/53901/1/AWI-DISSERTATION-2015.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs).The properties of the functional to minimize with respect to the given topology play an important role in the existence of minimizers of integral problems. We will introducethe important concepts of quasiconvexity and polyconvexity. Inspired by finite element methods from Numerical Analysis, we introduce a perturbed problem which has some surprising uniqueness properties.