Analytic stratifications and the cut locus of a class of distance functions |
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Authors: | Paolo Albano Antonio Bove |
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Institution: | (1) Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy;(2) Department of Mathematics, University of Illinois at Chicago, m/c 247, 851 S. Morgan St., 60607 Chicago, IL, USA |
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Abstract: | We study the analytic singularities of viscosity solutions of equations of eikonal type and obtain that the analytic singular
support of these functions has an analytic stratification. The singular support can be identified with the cut locus of the
distance to the boundary of an open set, when the interior is equipped with a degenerate Riemannian metric. We apply the result
to elliptic equations as well as to model operators of Grušin type. |
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Keywords: | |
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