Optimal semiconcavity with fractional modulus for Hamilton-Jacobi equations with Neumann boundary conditions

Here, we study the generalized semiconcavity property of viscosity solutions of the Neumann boundary value problem for Hamilton-Jacobi equations. In particular, we establish the global semiconcavity with a fractional modulus by investigating a regularity property of solutions to the Skorokhod problem, and show the optimality of the fractional exponent.