Article ID Journal Published Year Pages File Type
842050 Nonlinear Analysis: Theory, Methods & Applications 2011 5 Pages PDF
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)=〈A(x)p,p〉−1, 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 ∂Ω 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.
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Physical Sciences and Engineering Engineering Engineering (General)
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