Nonlocal Variational Principles with Variable Growth - Yongqiang Fu; Miaomiao Yang (Journal of Function Spaces)
This paper is concerned with the functional J defined by J(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, where Ω⊂ℝN is a regular open bounded set and W 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 of J.