Solutions of the Hamilton-Jacobi equation H(x,-Du(x)) = 1, where H(center dot, p) is Holder continuous and the level-sets {H(x, center dot) a parts per thousand currency sign 1} are convex and satisfy positive lower and upper curvature bounds, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the -regularity of the extremal trajectories associated with the multifunction generated by D (p) H.
Cannarsa, P., Cardaliaguet, P. (2012). Regularity results for eikonal-type equations with nonsmooth coefficients. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 19(6), 751-769 [10.1007/s00030-011-0150-1].
Regularity results for eikonal-type equations with nonsmooth coefficients
CANNARSA, PIERMARCO;
2012-01-01
Abstract
Solutions of the Hamilton-Jacobi equation H(x,-Du(x)) = 1, where H(center dot, p) is Holder continuous and the level-sets {H(x, center dot) a parts per thousand currency sign 1} are convex and satisfy positive lower and upper curvature bounds, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the -regularity of the extremal trajectories associated with the multifunction generated by D (p) H.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
