On the Eikonal equation for degenerate elliptic operators

Albano, Paolo

doi:10.1090/S0002-9939-2011-11132-8

On the Eikonal equation for degenerate elliptic operators
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Proc. Amer. Math. Soc. 140 (2012), 1739-1747 Request permission

Abstract:

We consider the nonnegative viscosity solution of the homogeneous Dirichlet problem for an eikonal equation associated to an operator sum of squares of vector fields of Grushin type in a symmetric domain. We show that the solution is locally Lipschitz continuous except at the characteristic boundary point. In the characteristic boundary point the solution has a Hölder regularity with exponent related to the Hörmander bracket condition. Finally, the singular set is an analytic stratification given by the characteristic boundary point and a half line.

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