Optimal Cwikel–Solomyak Estimates

Optimal Heat Kernel Estimates

Sharp smoothing estimates are proven for magnetic Schrr odinger semigroups in two dimensions under the assumption that the magnetic eld is bounded below by some positive constant B 0. As a consequence the L 1 norm of the associated integral kernel is bounded by the L 1 norm of the Mehler kernel of the Schrr odinger semigroup with the constant magnetic eld B 0 .

L∞-Estimates For Approximated Optimal Control Problems

An optimal control problem for a 2-d elliptic equation is investigated with pointwise control constraints. This paper is concerned with discretization of the control by piecewise linear functions. The state and the adjoint state are discretized by linear finite elements. Approximation of order h in the L-norm is proved in the main result.

Optimal a priori estimates for interface problems

Near-Optimal Coresets of Kernel Density Estimates

We construct near-optimal coresets for kernel density estimate for points in Rd when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size O( √ d log(1/ε)/ε), and we show a near-matching lower bound of size Ω( √ d/ε). The upper bound is a polynomial in 1/ε improvement when d ∈ [3, 1/ε2) (for all kernels except the Gaussian kernel which had a ...

On Global Hölder Estimates for Optimal Transportation

We generalize a well-known result of L. Caffarelli on Lipschitz estimates for optimal transportation T between uniformly log-concave probability measures. Let T : R → R be an optimal transportation pushing forward μ = e dx to ν = e dx. Assume that 1) the second differential quotient of V can be estimated from above by a power function, 2) modulus of convexity of W can be estimated from below by...