Related papers: Smooth compositions with a nonsmooth inner functio…
Aim of this paper is to develop a new technique, based on the Baire category theorem, in order to establish the closure of reachable sets and the existence of optimal trajectories for control systems, without the usual convexity…
Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of $C^1$ solutions of a class of iterative functional equations which involves iterates of the unknown functions and…
We study the maps between topological spaces whose composition with Baire class $\alpha$ maps also belongs to the $\alpha$'th Baire class and give characterizations of such maps
To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is…
The main result can be given a short and elementary proof which has been incorporated into Lemma 3.2 of arXiv:1206.5775
We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The integral functional is extended to the space of measures. The obtained second-order derivatives contain integrals on…
We give a simple way to extend index-theoretical statements from partial differential operators with smooth coefficients to operators with coefficients of finite Sobolev order.
In this paper we propose a higher non abelian cohomology theory without using the notion of n-category. We use this to study compositions series of affine manifolds and cohomology of manifolds.
Much of the vast literature on the integral during the last two centuries concerns extending the class of integrable functions. In contrast, our viewpoint is akin to that taken by Hassler Whitney [{\it Geometric integration theory},…
New classes of non-smooth bounded domains D, for which the embedding operator from H^1(D) into L^2(D) is compact are introduced. Examples are given and applications to scattering by rough obstacles are mentioned.
We generalize the Lebesgue-Hausdorff Theorem on the characterization of Baire-one functions for $\sigma$-strongly functionally discrete mappings defined on arbitrary topological spaces
A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems in the theory of functional spaces is the…
We prove a non-smooth generalization of the global implicit function theorem. More precisely we use the non-smooth local implicit function theorem and the non-smooth critical point theory in order to prove a non-smooth global implicit…
Categories of partial functions have become increasingly important principally because of their applications in theoretical computer science. In this note we prove that the category of partial bijections between sets as an…
In this paper, we prove a result on non-Baire sets in category bases which when applied together with a result of Grzegorek yeilds a comparatively stronger version of a decomposition theorem due to Ulam.
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the…
The phenomenon, known as "supersmoothness" was first observed for bivariate splines and attributed to the polynomial nature of splines. Using only standard tools from multivatiate calculus, we show that if we continuously glue two smooth…
We prove that for a stratifiable scattered space $X$ of finite scattered height, the function space $C_k(X)$ endowed with the compact-open topology is Baire if and only if $X$ has the Moving Off Property of Gruenhage and Ma. As a byproduct…
The functional equation $\varphi(Fx) - \varphi(x) = \gamma(x)$ is considered in topological, measurable and related categories from the point of view of functional analysis and general theory of dynamical systems. The material is presented…
In this paper we state and prove ad hoc "Separation Theorems" of the so-called Smooth Commutative Algebra, the Commutative Algebra of \(\mathcal{C}^{\infty}-\)rings. These results are formally similar to the ones we find in (ordinary)…