ﻻ يوجد ملخص باللغة العربية
Motivated by the almost completely open problem of characterizing unbounded coincidence sets of global solutions of the classical obstacle problem in higher dimensions, we give in this note a concise and easy-to-extend proof of the known fact that if the coincidence set ${u=0 }$ of a global solution $u$ is bounded with nonempty interior then it is an ellipsoid.
In this paper we give a full classification of global solutions of the obstacle problem for the fractional Laplacian (including the thin obstacle problem) with compact coincidence set and at most polynomial growth in dimension $N geq 3$. We do this i
We study a model for combustion on a boundary. Specifically, we study certain generalized solutions of the equation [ (-Delta)^s u = chi_{{u>c}} ] for $0<s<1$ and an arbitrary constant $c$. Our main object of study is the free boundary $partial{u>c
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.
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 give a direct analytic proof of the classical Boundary Harnack inequality for solutions to linear uniformly elliptic equations in either divergence or non-divergence form.