论文信息 - Maximal generalized solution of eikonal equation

Maximal generalized solution of eikonal equation

Abstract We study the Dirichlet problem for the eikonal equation: { 1 2 | ∇ u ( x ) | 2 − a ( x ) = 0 in Ω u ( x ) = φ ( x ) on ∂ Ω , without continuity assumptions on the map a ( ⋅ ) . We find a class of maps a ( ⋅ ) contained in the space L ∞ ( Ω ) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution.

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