We derive some higher order gradient estimates for the heat kernels on complete manifolds.
The proof of these results strongly relies on gradient estimates which are first established.
As an application, we obtain gradient estimates for the resolvent associated to the mild solution.
Even when the mechanism being optimized is unknown or not differentiable, optimization using high-variance or biased gradient estimates is still often the best strategy.
We establish uniform and optimal gradient estimates of solutions and prove that minimal solutions are non-degenerated.
we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions.
We use a coupling method to give gradient estimates for solutions to (12 Δ + Z u = 0 on a manifold.
Derivative formulae for heat semigroups are used to give gradient estimates for harmonic functions on regular domains in Riemannian manifolds.
Gradient estimates for Cheeger-harmonic functions and solutions to a class of non-linear Poisson type equations are presented.
The closed-loop LPV system matrices are factorised such that the effect of the scheduling parameter on the IFT gradient estimates can be compensated.
During the on-line execution phase, a certain quality of the gradient estimates is enforced through additional constraints in the optimization problem.
