In this paper, we consider an energy of the type Dirichlet energy plus potential term, for a map with values into a metric cone. We investigate the regularity of minimizers of such functionals, and prove that they are always locally Hölder continuous. We establish that Lipschitz continuity is achieved in some cases where the target space has non-positive curvature, and show examples for which t...

In this paper, we propose a new iteration method based on the hybrid steepest descent method and Ishikawa-type method for seeking a solution of a variational inequality involving a Lipschitz continuous and strongly monotone mapping on the set of common fixed points for a finite family of Lipschitz continuous and quasi-pseudocontractive mappings in a real Hilbert space. MSC: Primary 41A65; 47H17...

We show that local minimizers of functionals of the form Z Ω [f(Du(x)) + g(x , u(x))] dx, u ∈ u0 + W 1,p 0 (Ω), are locally Lipschitz continuous provided f is a convex function with p − q growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.

Let L be a divergence form operator with Lipschitz continuous coefficients in a domain Ω, and let u be a continuous weak solution of Lu= 0 in {u = 0}. In this paper, we show that if φ satisfies a suitable differential inequality, then vφ(x)= supBφ(x)(x)u is a subsolution of Lu= 0 away from its zero set. We apply this result to prove C1,γ regularity of Lipschitz free boundaries in two-phase prob...

The aim of paper is to prove a weak convergenceresult for finding a common of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. Using an example in C++, validity of the result will be proved. Also, we shall find a common element of the set of fixed points of a nonexpansive mapping and the ...

In this paper, we consider a class of nonsmooth, nonconvex constrained optimization problems where the objective function may be not Lipschitz continuous and the feasible set is a general closed convex set. Using the theory of the generalized directional derivative and the Clarke tangent cone, we derive a first order necessary optimality condition for local minimizers of the problem, and define...

We develop a constructive completion method in general Minkowski spaces, which successfully extends a completion procedure due to Bückner in twoand three-dimensional Euclidean spaces. We prove that this generalized Bückner completion is locally Lipschitz continuous, thus solving the problem of finding a continuous selection of the diametric completion mapping in finite dimensional normed spaces...

n be a continuous multifunction with compact, not necessarily convex values. If F is Lipschitz continuous, it was shown in [4] that there exists a measurable selection f of F such that, for every x 0 , the Cauchy problem ˙ x(t) = f (t, x(t)), x(0) = x 0 has a unique Caratheodory solution, depending continuously on x 0. In this paper, we prove that the above selection f can be chosen so that f (...

A metric compact space M is seen as the closure of the union of a sequence (Mn) of finite n-dense subsets. Extending to M (up to a vanishing uniform distance) Banach-space valued Lipschitz functions defined on Mn, or defining linear continuous near-extension operators for real-valued Lipschitz functions on Mn, uniformly on n is shown to be equivalent to the bounded approximation property for th...

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.