Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4612497 | Journal of Differential Equations | 2007 | 28 Pages |
Abstract
Given a bounded domain ΩâRd and two integro-differential operators L1, L2 of the form Lju(x)=p.v.â«Î©(u(x)âu(y))kj(x,y,xây)dy we study the fully nonlinear Bellman equation(0.1)maxj=1,2{Lju(x)+aj(x)u(x)âfj(x)}=0in Ω, with Dirichlet boundary conditions. Here, aj,fj:ΩâR are non-negative functions. We prove the existence of a non-negative function u:ΩâR which satisfies (0.1) almost everywhere. The main difficulty arises through the nonlocality of Lj and the absence of regularity near the boundary.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
H. Abels, M. Kassmann,