Twenty years ago David and Journé discovered a criterion for the continuity on L of Calderón-Zygmund operators defined by singular integrals. In their approach the distributional kernel of the given operator is locally Hölder continuous outside the diagonal. The aim of this paper is to prove a David-Journé theorem where this smoothness assumption is replaced by a weaker one. Our approach strong...

We combine a maximum principle for vector-valued mappings established by D’Ottavio, Leonetti and Musciano [DLM] with regularity results from [BF3] and prove the Hölder continuity of the first derivatives for local minimizers u: Ω → RN of splitting-type variational integrals provided Ω is a domain in R2. Roughly speaking, anisotropic variational integrals ∫ Ω F (∇u) dx with integrand F (∇u) of (...

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Hölder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity o...

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper Hölder type, respectively, hold. Furthermore, we apply the ...

Controllability of finite dimensional linear systems can be decided via a finite number of matrix operations, with an a-priori known bound on this number of operations. For both polynomial and general nonlinear analytic systems that are affine in the control it remains an open problem whether controllability can at all be decided by a finite number of differentiations of the data. This is close...

The triangular ratio metric is studied in a domain G⊊Rn, n≥2. Several sharp bounds are proven for this metric, especially the case where unit disk of complex plane. results applied to study Hölder continuity quasiconformal mappings.

A maximum principle and some a priori estimates of a class of degenerate equations with X-ellipticity in the sense of distributions are established. A local comparison of the generalized Green function with its fundamental solutions is obtained. As an application, by means of the power of the Green function as a kernel function of a local integral, we also derive local Hölder continuity for non...

We prove that under some global conditions on the maximum and the minimum eigenvalue of the matrix of the coefficients, the gradient of the (weak) solution of some degenerate elliptic equations has higher integrability than expected. Technically we adapt the Giaquinta-Modica regularity method in some degenerate cases. When the dimension is two, a consequence of our result is a new Hölder contin...