Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients

Details Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients

2011-03-23

arxiv.org/abs/1103.4454v1

Mathematics

Optimization and Control

Scientific paper

Solutions of the Hamilton-Jacobi equation $H(x,-Du(x))=1$, with $H(\cdot,p)$
H\"older continuous and $H(x,\cdot)$ convex and positively homogeneous of
degree 1, are shown to be locally semiconcave with a power-like modulus. An
essential step of the proof is the ${\mathcal C}^{1,\alpha}$-regularity of the
extremal trajectories associated with the multifunction generated by $D_pH$.

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