相关论文: A Class of Functionals on the Sequence Space $s$ S…

Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\subseteq T \text{ if and only if…

In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients…

Whenever the defining sequence of a Carleman ultraholomorphic class (in the sense of H. Komatsu) is strongly regular and associated with a proximate order, flat functions are constructed in the class on sectors of optimal opening. As…

Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…

The present paper is devoted to analysis of the lack of compactness of bounded sequences in \emph{inhomogeneous} Sobolev spaces, where bounded sequences might fail to be compact due to an isometric group action, that is, \emph{translation}.…

We present an extension of the classical De Giorgi class, and then we show that functions in this new class are locally bounded and locally H\"older continuous. Some applications are given. As a first application, we give a regularity…

We establish a Fenchel-Moreau type theorem for proper convex functions $f\colon X\to \bar{L}^0$, where $(X, Y, \langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\bar L^0$ is the space of all extended real-valued functions…

One of the most important issues for the frequent special functions is the uniqueness conditions of such functions. As far as we know, there are no characterizations for the floor, ceiling, and fractional part functions in general (as real…

The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…

In this paper, we propose necessary and sufficient conditions for a scalar function to be nonincreasing along solutions to general differential inclusions with state constraints. The problem of determining if a function is nonincreasing…

Let f be local diffeomorphism between real Banach spaces. We prove that if the locally Lipschitz functional F(x)=1/2|f(x)-y|^2 satisfies the Chang Palais-Smale condition for all y in the target space of f, then f is a norm-coercive global…

We extend the notion of the smallest volume ellipsoid containing a convex body in~$\mathbb{R}^{d}$ to the setting of logarithmically concave functions. We consider a vast class of logarithmically concave functions whose superlevel sets are…

We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…

Generators of the algebra of first class functions in a system with second class constraints are found. It is shown that first class functions form algebras with respect to the Dirac bracket and pointwise multiplication.The subspace of…

For variational problems with $O(N)$-symmetry the existence of several geometrically distinct solutions had been shown by use of group theoretic approach in previous articles. It was done by a crafty choice of a family $H_i \subset O(N)$…

In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…

We consider a space of infinitely smooth functions on an unbounded closed convex set in ${\mathbb R}^n$. It is shown that each function of this space can be extended to an entire function in ${\mathbb C}^n$ satisfying some prescribed growth…

This paper introduces a novel generalization of the classical concept of $S$-metric spaces, referred to as composed $S$-metric spaces. By incorporating a composed function, we impose more general conditions on the triangle inequality,…

By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…

We show that the Hamiltonian action satisfies the Palais-Smale condition over a "mixed regularity" space of loops in cotangent bundles, namely the space of loops with regularity $H^s$, $s\in (\frac 12, 1)$, in the base and $H^{1-s}$ in the…