We prove the local Hölder continuity of strong local minimizers of the stored energy functional E(u) = ∫ Ω λ|∇u|2 + h(det∇u) dx subject to a condition of ‘positive twist’. The latter turns out to be equivalent to requiring that u maps circles to suitably star-shaped sets. The convex function h(s) grows logarithmically as s → 0+, linearly as s → +∞, and satisfies h(s) = +∞ if s ≤ 0. These proper...

Abstract. We study a matrix-valued Schrödinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that away from a discrete set its Lyapunov exponents do not vanish. For this we use a criterion by Gol’dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer ma...

We study the sample path regularity of the solutions of a class of spde’s which are second order in time and that includes the stochastic wave equation. Non-integer powers of the spatial Laplacian are allowed. The driving noise is white in time and spatially homogeneous. Continuing with the work initiated in Dalang and Mueller (2003), we prove that the solutions belong to a fractional L2-Sobole...

We develop the L p-theory of the spectral shift function, for p ≥ 1, applicable to pairs of self-adjoint operators whose difference is in the trace ideal I p , for 0 < p ≤ 1. This result is a key ingredient of a new, short proof of the Wegner estimate applicable to a wide variety of additive and multiplicative random perturbations of deterministic background operators. The proof yields the corr...

In this paper, by using a weaker assumption, we discuss the Hölder continuity of solution maps for two cases of parametric generalized vector equilibrium problems under the case that the solution map is a general set-valued one, but not a single-valued one. These results extend the recent ones in the literature. Several examples are given for the illustration of our results.