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 a one-dimensional moving-boundary problem for the time-fractional diffusion equation, where the time-fractional derivative of order α. ∈. (0, 1) is taken in the Caputo sense. A generalization of the Hopf lemma ...

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 ...

We introduce and analyze a nonlocal free boundary problem which may be of interest to describe the spreading of populations in hostile environments. The rate of growth of the volume of the region occupied by the population ...

We obtain for the two-phase Lamé-Clapeyron-Stefan problem for a semi-infinite material an equivalence between the temperature and convective boundary conditions at the fixed face in the case that an inequality for the ...

One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face x=0, variable in time, is considered. Throught several transformations the problem is reduced ...

We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x> 0 , with phase change temperature Tf. We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. A ...

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 ...