In this paper we study a one phase free boundary problem for the p (x)-Laplacian with non-zero right hand side. We prove that the free boundary of a weak solution is a C1,α surface in a neighborhood of every "flat" free ...

We consider viscosity solutions to a one-phase free boundary problem for the p(x)-Laplacian with non-zero right hand side. We apply the tools developed in De Silva (2011) to prove that flat free boundaries are C1,α. Moreover, ...

We consider an optimization problem with volume constraint for an energy functional associated to an inhomogeneous operator with nonstandard growth. By studying an auxiliary penalized problem, we prove existence and ...

In this paper we address a one phase minimization problem for a functional that includes the perimeter of the positivity set. It also includes three terms, the first one is ∫fu and the second ∫u>0h where f and h are bounded ...

We consider the optimization problem of minimizing ∫Ω frac(1, p (x)) | ∇ u |p (x) + λ (x) χ{u > 0} d x in the class of functions W1, p ({dot operator}) (Ω) with u - φ0 ∈ W01, p ({dot operator}) (Ω), for a given φ0 ≥ 0 and ...