Hölder Continuous Regularity of Stochastic Convolutions with Distributed Delay

improved regularity of harmonic map flows with hölder continuous energy ∗

For a smooth harmonic map flow u : M× [0, T ) → N with blow-up as t ↑ T , it has been asked ([6], [5], [7]) whether the weak limit u(T ) : M→ N is continuous. Recently, in [12], we showed that in general it need not be. Meanwhile, the energy function E(u(·)) : [0, T ) → R, being weakly positive, smooth and weakly decreasing, has a continuous extension to [0, T ]. Here we show that if this exten...

Directional Hölder Metric Regularity

This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Hölder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directi...

Regularity of Solutions to Stochastic Volterra Equations with Infinite Delay

The paper gives necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a ddimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used.

Hölder Stable Minimizers, Tilt Stability, and Hölder metric Regularity of Subdifferentials

Using techniques of variational analysis and dual techniques for smooth conjugate functions, for a local minimizer of a proper lower semicontinuous function f on a Banach space, p ∈ (0, +∞) and q = 1+p p , we prove that the following two properties are always equivalent: (i) x̄ is a stable q-order minimizer of f and (ii) x̄ is a tilt-stable p-order minimizer of f . We also consider their relation...

Regularity of stochastic delay equations under pth order degeneracy