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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, ...
Hopf lemma for the fractional diffusion operator and its application to a fractional free-boundary problem
(Academic Press Inc Elsevier Science, 2016-02)
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 ...
Symmetric simple exclusion process with free boundaries
(Springer, 2015-02)
We consider the one dimensional symmetric simple exclusion process with additional births and deaths restricted to a subset of configurations where there is a leftmost hole and a rightmost particle. At a fixed rate birth ...
The radial integration method applied to dynamic problems of anisotropic plates
(John Wiley & Sons LtdChichesterInglaterra, 2007)
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 ...
A nonlocal diffusion problem with a sharp free boundary
(European Mathematical Society, 2019-12)
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 ...
A Compactness Theorem and Some Gap Results for Free Boundary Minimal Surfaces
(Universidade Federal de Minas GeraisUFMG, 2017-08-25)
This thesis consists of several results about minimal surfaces. In the first part we study free boundary minimal surfaces in the Euclidean ball B^n. We prove that if (...) is a kdimensional free boundary minimal surface ...
Nonlinear problems with solutions exhibiting a free boundary on the boundary
(GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2005)
On a variational principle for shape optimization and elliptic free boundary problemsOn a variational principle for shape optimization and elliptic free boundary problems
(Universidad de Costa Rica, Centro de Investigación en Matemática Pura y Aplicada (CIMPA), 1999)