Characterisation of the weak lower semicontinuity for a type of nonlocal integral functional: The n-dimensional scalar case.
2009 - J. Muñoz
Journal of Mathematical Analysis and Applications, 360, 495-502 (2009)
Muñoz Martín, Julio.
In this work we are going to prove the functional J defined by View the MathML source is weakly lower semicontinuous in W1,p(Ω) if and only if W is separately convex. We assume that Ω is an open set in View the MathML source and W is a real-valued continuous function fulfilling standard growth and coerciveness conditions. The key to state this equivalence is a variational result established in terms of Young measures.