The Distance Function to the Boundary, Finsler Geometry, and the Singular Set of Viscosity Solutions of Some Hamilton-Jacobi Equations
نویسندگان
چکیده
(1.4) H(x,∇u) = 1 in . Under suitable conditions we show that the (n−1)–dimensional Hausdorff measure of the singular set of solutions (the complement of the open set where u ∈ C) is finite. In addition, we prove the corresponding result for H(x, t, p) but under very special conditions. See Theorem 10.5 and its simple consequences, Propositions 1.8, 1.10, and 1.11. We were brought to the problem by first studying the singular set of the distance function to the boundary of . This set is sometimes called the ridge of , or medial axes. Our interest in the set arises in connection with nonlinear elliptic boundary value problems [11]. We first describe this set .
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