ﻻ يوجد ملخص باللغة العربية
We consider the vectorial analogue of the thin free boundary problem introduced in cite{CRS} as a realization of a nonlocal version of the classical Bernoulli problem. We study optimal regularity, nondegeneracy, and density properties of local minimizers. Via a blow-up analysis based on a Weiss type monotonicity formula, we show that the free boundary is the union of a regular and a singular part. Finally we use a viscosity approach to prove $C^{1,alpha}$ regularity of the regular part of the free boundary.
In this paper, we proceed to study the nonlocal diffusion problem proposed by Li and Wang [8], where the left boundary is fixed, while the right boundary is a nonlocal free boundary. We first give some accurate estimates on the longtime behavior by c
We consider a free boundary problem on cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. We show that when the cone is three-dimensional and c is large enough, the free boundary avoid
In this paper we consider a free boundary problem which models the spreading of an invasive species whose spreading is enhanced by the changing climate. We assume that the climate is shifting with speed c and obtain a complete classification of the l
We consider a free boundary problem on three-dimensional cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. Combining analysis and computer-assisted proof, we show that when c is less
The parabolic obstacle problem for the fractional Laplacian naturally arises in American option models when the assets prices are driven by pure jump Levy processes. In this paper we study the regularity of the free boundary. Our main result establis