Perron's solutions for two-phase free boundary problems with distributed sources

We use Perron method to construct a weak solution to a two-phase free boundary problem with right-hand-side. We thus extend the results of the pioneer work of Caffarelli for the homogeneous case

Solution Map Analysis of a Multiscale Drift-Diffusion Model for Organic Solar Cells

In this article we address the theoretical study of a multiscale drift-diffusion (DD) model for the description of photoconversion mechanisms in organic solar cells. The multiscale nature of the formulation is based on the co-presence of light absorption, conversion and diffusion phenomena that occur in the three-dimensional material bulk, of charge photoconversion phenomena that occur at the two-dimensional material interface separating acceptor and donor material phases, and of charge separation and subsequent charge transport in each three-dimensional material phase to device terminals that are driven by drift and diffusion electrical forces. The model accounts for the nonlinear interaction among four species: excitons, polarons, electrons and holes, and allows to quantitatively predict the electrical current collected at the device contacts of the cell. Existence and uniqueness of weak solutions of the DD system, as well as nonnegativity of all species concentrations, are proved in the stationary regime via a solution map that is a variant of the Gummel iteration commonly used in the treatment of the DD model for inorganic semiconductors. The results are established upon assuming suitable restrictions on the data and some regularity property on the mixed boundary value problem for the Poisson equation. The theoretical conclusions are numerically validated on the simulation of three-dimensional problems characterized by realistic values of the physical parameters

On the Harnack inequality for non-divergence parabolic equations

In this paper we propose an elementary proof of the Harnack inequality for linear parabolic equations in non-divergence form

Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems

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Il problema di Stefan: regolarità della frontiera libera

We describe recent results on the regularity for the Stefan problem obtained in a joint work with I. Athanasopoulos and L. Caffarelli

Recent Results on Nonlinear Elliptic Free Boundary Problems

In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.Fil: Ferrari, Fausto. Universidad de Bologna; ItaliaFil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Salsa, Sandro. Politecnico di Milano; Itali

Regularity of transmission problems for uniformly elliptic fully nonlinear equations

We investigate the regularity of transmission problems for a general class of uniformly elliptic fully non linear equations. We prove that, if the forcing term is Lipschitz, then viscosity solution are C1,\u3b3

Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary