Compactness of minimizing sequences. (May 2016) - Boccardo, Lucio; Gallouet, Thierry
Abstract: We consider a minimization problem of a functional in the space W 0 1, p ( Ω ), where 1 < p < + ∞ and Ω is a bounded open set of R N . We prove the compactness, in the space W 0 1, p ( Ω ), under convenient hypotheses, of a minimizing sequence. The main difficulty is to prove the convergence in measure of the gradient of the minimizing sequence. Furthermore, considering a sequence of minimization problems in the space W 0 1, p ( Ω ), we prove some convergence results of the sequence of minimizers to the minimizer of the limit problem.