Nonlocal Variational Principles with Variable Growth. (7th April 2014) - Fu, Yongqiang; Yang, Miaomiao
Abstract : This paper is concerned with the functionalJ defined byJ ( u ) = ∫ Ω × Ω W ( x, y, ∇ u ( x ), ∇ u ( y ) ) d x d y, whereΩ ⊂ ℝ N is a regular open bounded set andW is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation ofJ .