Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842050 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 5 Pages |
Abstract
We consider the viscosity solution of a homogeneous Dirichlet problem for the eikonal equation in a bounded set Ω. We suppose that the Hamiltonian, H(x,p)=ãA(x)p,pãâ1, is strictly convex w.r.t. the variables p and of class C1,1 w.r.t. the variables x. Then the solution of the Dirichlet problem admits an extension to a neighbourhood of Ω, u¯, such that u¯ is still a viscosity solution of the eikonal equation if and only if âΩ satisfies an exterior sphere condition. The above result, in particular, provides a characterization of the boundary singularities and a regularity theorem (up to the boundary) for the solution of the eikonal equation.
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Paolo Albano,