Nonlocal Variational Principles with Variable Growth. (7th April 2014)

• Record Type: Journal Article
• Authors: Fu, Yongqiang; Yang, Miaomiao
• Other Names: Bu Qingying Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-04-07
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/435247
• Languages: English
• ISSNs: 2314-8896

Abstract

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 .