A Minimum Problem with Free Boundary for the p(x)−Laplace Operator
Abdeslem Lyaghfouri · Advanced Nonlinear Studies · 2011
Abstract In this paper we consider the problem of minimizing the functional We prove Lipschitz continuity for each minimizer u and establish the nondegeneracy at the free boundary (∂[u > 0]) ∩ Ω and the locally uniform positive density of the sets [u > 0] and [u = 0]. In particular we obtain that the Lebesgue measure of the free boundary is zero.