We study the applicability of the the method of layer potentials, in the treatment of boundary value problems for the Laplace-Beltrami operator on Lipschitz subdomains of Riemannian manifolds, in the case when metric tensor gjkdxj ⊗ dxk has low regularity. Under the assumption that |gjk(x) − gjk(y)| ≤ C ω(|x − y|), where the modulus of continuity ω satisfies a Dini type condition, we prove the ...

For a lower semicontinuous function f on a Banach space X, we study the existence of a positive scalar μ such that the distance function dS associated with the solution set S of f(x) ≤ 0 satisfies dS(x) ≤ μmax{f(x), 0} for each point x in a neighborhood of some point x0 in X with f(x) < for some 0 < ≤ +∞. We give several sufficient conditions for this in terms of an abstract subdifferential and...

For all n large enough, we show uniqueness of a critical point in best rational approximation of degree n, in the L2-sense on the unit circle, to functions of the form f(z) = ∫ dμ(t ) z − t + r (z), dμ= μ̇dω[a,b], with r a rational function and μ̇ a complex-valued Dini-continuous function on a real segment [a, b] ⊂ (−1,1) which does not vanish, and whose argument is of bounded variation. Here ω[a...

We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints such that all functions are, at least, Dini differentiable (in some cases, Hadamard differentiable and sometimes, quasiconvex). Several constraint qualifications are given in such a way that generalize both the qualifications introduced by Maeda and the classical ones, when the f...

We achieve on self-affine Sierpinski carpets the multifractal analysis of the Birkhoff averages of potentials satisfying a Dini condition. Given such a potential, the corresponding Hausdorff spectrum cannot be deduced from that of the associated Gibbs measure by a simple transformation. Indeed, these spectra are respectively obtained as the Legendre transform of two distinct concave differentia...

The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by the means of the proximal subdifferential of the no...

The present paper provides first and second-order characterizations of a radially lower semicontinuous strictly pseudoconvex function f : X → R defined on a convex setX in the real Euclidean space Rn in terms of the lower Dini-directional derivative. In particular we obtain connections between the strictly pseudoconvex functions, nonlinear programming problem, Stampacchia variational inequality...

Terasem, transhümanizmin insanı dönüştürme ideallerine etik, hukuki ve dini bağlamında yaklaşan hem tekno-fütürist de transhümanist bir harekettir. İnsan olmayı dünyevi tecrübeler anılardan ibaret gören ölümsüzlüğün bu deneyim bilgilerin kaydedilmesi beyinle benzer şekilde işlenebilmesi ile mümkün olacağını iddia etmektedir. Ruhu yok sayarak insana ait yaşanmışlıkların tecrübelerin dijital kopy...

In this work we introduce for extended real valued functions, defined on a Banach space X, the concept of K directionally Lipschitzian behavior, where K is a bounded subset of X. For different types of sets K (e.g., zero, singleton, or compact), the K directionally Lipschitzian behavior recovers well-known concepts in variational analysis (locally Lipschitzian, directionally Lipschitzian, or co...

In this paper, we give some new generalized convexities with the tool–right upper-Diniderivative which is an extension of directional derivative. Next, we establish not only Karush-KuhnTucker necessary but also sufficient optimality conditions for mathematical programming involving new generalized convex functions. In the end, weak, strong and converse duality results are proved to relate weak ...