ﻻ يوجد ملخص باللغة العربية
In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish structural properties of the free boundary.
In this paper, motivated by a problem arising in random homogenization theory, we initiate the study of uniform estimates for the fractional penalized obstacle problem, $ Delta^{s}u^{epsilon} = beta_{epsilon} (u^{epsilon})$. In particular we consider
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
We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.
We study the regularity of the free boundary in the obstacle for the $p$-Laplacian, $minbigl{-Delta_p u,,u-varphibigr}=0$ in $Omegasubsetmathbb R^n$. Here, $Delta_p u=textrm{div}bigl(| abla u|^{p-2} abla ubigr)$, and $pin(1,2)cup(2,infty)$. Near th
The goal of this paper is to establish generic regularity of free boundaries for the obstacle problem in $mathbb R^n$. By classical results of Caffarelli, the free boundary is $C^infty$ outside a set of singular points. Explicit examples show that th