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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the Eikonal equation for degenerate elliptic operators

Author: Paolo Albano
Journal: Proc. Amer. Math. Soc. 140 (2012), 1739-1747
MSC (2010): Primary 35F30, 35F21, 35D40
Posted: September 22, 2011
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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.

References

Bibliography

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