$\Gamma$-convergence for power-law functionals with variable exponents

Francesca Prinari, Michela Eleuteri

We study the $\Gamma$-convergence of the functionals $F_n(u):=||f(\cdot ,u(\cdot ),Du(\cdot ))|{|}_{p_n(\cdot )}$ and ${\mathcal{F}}_n(u):={\int }_{\Omega }\frac{1}{p_n(x)}{f}^{p_n(x)}(x,u(x),Du(x))dx$…