An extension problem related to the fractional Laplacian
L Caffarelli, L Silvestre - Communications in partial differential …, 2007 - Taylor & Francis
The operator square root of the Laplacian (−▵) 1/2 can be obtained from the harmonic
extension problem to the upper half space as the operator that maps the Dirichlet boundary …
extension problem to the upper half space as the operator that maps the Dirichlet boundary …
Regularity estimates for the solution and the free boundary of 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 …
an appropriate differential equation to study its obstacle problem. We write an equivalent …
Obstacle problems and free boundaries: an overview
X Ros-Oton - SeMA Journal, 2018 - Springer
Free boundary problems are those described by PDEs that exhibit a priori unknown (free)
interfaces or boundaries. These problems appear in physics, probability, biology, finance, or …
interfaces or boundaries. These problems appear in physics, probability, biology, finance, or …
Nonlinear porous medium flow with fractional potential pressure
LA Caffarelli, JL Vazquez - arXiv preprint arXiv:1001.0410, 2010 - arxiv.org
We study a porous medium equation, with nonlocal diffusion effects given by an inverse
fractional Laplacian operator. We pose the problem in n-dimensional space for all t> 0 with …
fractional Laplacian operator. We pose the problem in n-dimensional space for all t> 0 with …
Nonlinear diffusion with fractional Laplacian operators
JL Vázquez - Nonlinear partial differential equations: the Abel …, 2012 - Springer
We describe two models of flow in porous media including nonlocal (long-range) diffusion
effects. The first model is based on Darcy's law and the pressure is related to the density by …
effects. The first model is based on Darcy's law and the pressure is related to the density by …
[图书][B] Integro-differential elliptic equations
X Fernández-Real, X Ros-Oton - 2024 - Springer
Progress in Mathematics is a series of books intended for professional mathematicians and
scientists, encompassing all areas of pure mathematics. This distinguished series, which …
scientists, encompassing all areas of pure mathematics. This distinguished series, which …
Generic regularity of free boundaries for the obstacle problem
The goal of this paper is to establish generic regularity of free boundaries for the obstacle
problem in R n R^n. By classical results of Caffarelli, the free boundary is C∞ C^∞ outside a …
problem in R n R^n. By classical results of Caffarelli, the free boundary is C∞ C^∞ outside a …
The obstacle problem for nonlinear integro-differential operators
J Korvenpää, T Kuusi, G Palatucci - Calculus of Variations and Partial …, 2016 - Springer
We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal,
possibly degenerate, integro-differential operators, whose model is the fractional p …
possibly degenerate, integro-differential operators, whose model is the fractional p …
On the fine structure of the free boundary for the classical obstacle problem
In the classical obstacle problem, the free boundary can be decomposed into “regular” and
“singular” points. As shown by Caffarelli in his seminal papers (Caffarelli in Acta Math 139 …
“singular” points. As shown by Caffarelli in his seminal papers (Caffarelli in Acta Math 139 …
Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem
N Garofalo, A Petrosyan - Inventiones mathematicae, 2009 - Springer
We construct two new one-parameter families of monotonicity formulas to study the free
boundary points in the lower dimensional obstacle problem. The first one is a family of Weiss …
boundary points in the lower dimensional obstacle problem. The first one is a family of Weiss …