We describe a method of obtaining closed-form complete solutions of certain second-order linear partial differential equations with more than two independent variables. This method generalizes the classical method of Laplace transformations of second-order hyperbolic equations in the plane and is based on an idea given by Ulisse Dini in 1902.

The relationships between the generalized directional derivative of the distance function and the existence of nearest points as well as some geometry properties in Banach spaces are studied. It is proved in the present paper that the condition that for each closed subset G of X and x ∈ X \ G, the Clarke, Michel-Penot, Dini or modified Dini directional derivative of the distance function is 1 o...

In [2] Fan and Pollicott gave an estimate of convergence speed of the iterations fSn g fgn=1 ( Sg being the Ruelle operator de ̄ned by a normalized summable variation potential function g on a subshift of ̄nite type.) Later on Fan and Jiang [1] extended it to locally expansive Dini dynamical system. It is known that the systems they considered have the bounded distortion property (BDP). We extend...

It is essential for the strategy of open access self-archiving that scientific authors are given comprehensive information on publisher copyright policies. DINI, the German Initiative for Networked Information, has developed a German (and potentially multilingual) interface to the English SHERPA/RoMEO service to provide additional information on German publishers' open access policies. As a nex...

Andrea Caiti, Vincenzo Calabrò, and Andrea Munafò Inter-university Ctr. on, Integrated Systems for the Marine Environment, Research Center “E.Piaggio”, Dept. of Energy and Systems Engineering, University of Pisa Pisa, 56127, Italy e-mail: [email protected], [email protected], [email protected] Gianluca Dini Inter-university Ctr. on, Integrated Systems for the Marine Environment, Rese...

In this paper we first provide a general formula of inclusion for the DiniHadamard ε-subdifferential of the difference of two functions and show that it becomes equality in case the functions are directionally approximately starshaped at a given point and a weak topological assumption is fulfilled. To this end we give a useful characterization of the Dini-Hadamard ε-subdifferential by means of ...

A new characterization of bivariate copulas is given by using the notion of Dini derivatives. Several examples illustrate the usefulness of this result.

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend variou...

— In 1964 J. Serrin proposed the following conjecture. Let u ∈ W1,1 loc (Ω) be a weak solution of the second order elliptic equation (1) below, in divergence form, with Hölder continuous coefficients aij (x); then u is a “classical” solution. We announce a solution of this conjecture assuming only u ∈ BVloc(Ω) and Dini continuous coefficients.