Article ID Journal Published Year Pages File Type
4610422 Journal of Differential Equations 2014 33 Pages PDF
Abstract

We study the Dirichlet problem for the eikonal equation:{12|∇u(x)|2−a(x)=0inΩu(x)=φ(x)on∂Ω, without continuity assumptions on the map a(⋅)a(⋅). We find a class of maps a(⋅)a(⋅) contained in the space L∞(Ω)L∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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