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Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian
(European Mathematical Society, 2017-04)
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 ...
Regularity of flat free boundaries for a p(x)-Laplacian problem with right hand side
(Pergamon-Elsevier Science Ltd, 2021-11)
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, ...
Relationship between Neumann solutions for two-phase Lamé-Clapeyron-Stefan problems with convective and temperature boundary conditions
(Vinca Inst Nuclear Sci, 2017-01)
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 ...
Uniqueness of solution to a free boundary problem from combustion
(American Mathematical Society, 2001-04)
We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x, t) ≥ 0, ...
Gradient estimates for viscosity solutions of singular fully nonlinear elliptic equations
(Academic Press Inc Elsevier ScienceSan DiegoEUA, 2010)
Nonlinear problems with solutions exhibiting a free boundary on the boundary
(GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2005)
A Free Boundary Model for Oxygen Diffusion in A Spherical Medium
(World Scientific, 2015-08)
The goal of this article is to find a correct approximated solution using a polynomial of sixth degree for the free boundary problem corresponding to the diffusion of oxygen in a spherical medium with simultaneous absorption ...
Determination of unknown thermal coefficients in a Stefan problem for Storm’s type materials
(Sociedade Brasileira de Matemática Aplicada e Computacional, 2018-09)
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 ...
Nonlinear problems with solutions exhibiting a free boundary on the boundary
(GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2005)
We prove existence of nonnegative solutions to -Delta u + u = 0 on a smooth bounded domain Omega subject to the singular boundary derivative condition partial derivative u/partial derivative v = -u(-beta) + lambda f (x, ...
An optimization problem with volume constraint for an inhomogeneous operator with nonstandard growth
(American Institute of Mathematical Sciences, 2021-06)
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 ...