We consider the problem of minimizing the Lagrangian ∫ [F (∇u)+f u] among functions on Ω ⊂ R with given boundary datum φ. We prove Lipschitz regularity up to the boundary for solutions of this problem, provided Ω is convex and φ satisfies the bounded slope condition. The convex function F is required to satisfy a qualified form of uniform convexity only outside a ball and no growth assumptions ...

In this paper we prove the SBV regularity of the distributional derivative of a viscosity solution of the Hamilton-Jacobi equation ∂tu + H(t, x, Dxu) = 0 in Ω ⊂ [0, T ]× R, under the hypothesis of uniform convexity of the Hamiltonian H in the last variable. This result extends the result of Bianchini, De Lellis and Robyr obtained for an Hamiltonian H = H(Dxu) which depends only on the spatial d...

We study geometrical conditions guaranteeing the validity of the classical GaffneyFriedrichs estimate ‖u‖H1,2(Ω) ≤ C ( ‖du‖L2(Ω) + ‖δu‖L2(Ω) + ‖u‖L2(Ω) ) (0.1) granted that the differential form u has a vanishing tangential or normal component on ∂Ω. Our main result is that (0.1) holds provided Ω satisfies a suitable convexity assumption. In the Euclidean setting, a uniform exterior ball condit...

This technical report is a companion to [5] that proves the diagonal blocks of the Hessian matrix for the inverse mean-ratio metric for tetrahedral elements are positive definite. Thus, the block Jacobi preconditioner used in the inexact Newton method to solve the mesh shape-quality optimization problem using the average inverse mean-ratio metric for the objective function is positive definite....

We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejér monotonicity where the convergence uses the compactness of the underlying set. These quantitative versions are in the form of explicit rates of so-called metastability in the sense of T. Tao. Our approach covers examples ranging from the proximal p...

We prove that a closed, geodesically convex subset C of P 2 (R) is closed with respect to weak convergence in P 2 (R). This means that if (μn) ⊂ C is such that μn ⇀ μ in duality with continuous bounded functions and supn ∫ |x|dμn <∞, then μ ∈ C as well.

We extend a result of Minsky to show that for a map of a surface to a hyperbolic 3-manifold which is not necessarily π1-injective but is 2-incompressible rel a geodesic link with a definite tube radius, the set of noncontractible simple loops with a bounded length representatives is quasi-convex in the complex of curves.

The aim of the present paper is to consider geometric properties such as starlikeness and convexity of the Cesáro partial sums of certain analytic functions in the open unit disk. By using the Cesáro partial sums, we improve some recent results including the radius of convexity. 1 Introduction Let U := {z : |z| < } be a unit disk in the complex plane C and let H denote the space of all analyti...

This paper presents an analysis of the problem of aggregating preference orderings under subjective uncertainty. Individual preferences, or opinions, agree on the ranking of risky prospects, but are quite general because we do not specify the perception of ambiguity or the attitude towards it. A convexity axiom for the ex-ante preference characterizes a (collective) decision rule that can be in...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...