Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients

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 $D_pH$.

💡 Research Summary

The paper investigates regularity properties of viscosity solutions to the eikonal‑type Hamilton‑Jacobi equation
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