$\Gamma$-convergence of some super quadratic functionals with singular weights

Giampiero Palatucci, Yannick Sire

We study the $\Gamma$-convergence of the following functional ($p>2$) $$ F_ε(u):=ε^{p-2}\int_Ω|Du|^p d(x,\partial Ω)^{a}dx+\frac{1}{ε^{\frac{p-2}{p-1}}}\int_ΩW(u) d(x,\partial Ω)^{-\fra…