Related papers: Generalized Jacobian for Functions with Infinite D…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
A classical result in the study of Ginzburg-Landau equations is that, for Dirichlet or Neumann boundary conditions, if a sequence of functions has energy uniformly bounded on a logarithmic scale then we can find a subsequence whose…
In this article we study maps with nilpotent Jacobian in $\mathbb{R}^n$ distinguishing the cases when the rows of $JH$ are linearly dependent over $\mathbb{R}$ and when they are linearly independent over $\mathbb{R}.$ In the linearly…
This paper is concerned with generalizations of the notion of principal eigenvalue in the context of space-time periodic cooperative systems. When the spatial domain is the whole space, the Krein-Rutman theorem cannot be applied and this…
This work introduces the class of generalized linear-quadratic functions, constructed using maximally monotone symmetric linear relations. Calculus rules and properties of the Moreau envelope for this class of functions are developed. In…
A further significant extension is presented of the infinitely large class of differential algebras of generalized functions which are the basic structures in the nonlinear algebraic theory listed under 46F30 in the AMS Mathematical Subject…
For the numerical solution of nonsmooth problems, sometimes it is not necessary that an exact subgradient/generalized Jacobian is at our disposal, but it suffices that a semismooth derivative, i.e., a mapping satisfying a certain…
We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without…
The classical Mountain Pass Lemma of Ambrosetti-Rabinowitz has been studied, extended and modified in several directions. Notable examples would certainly include the generalization to locally Lipschitz functionals by K.C. Chang, analyzing…
We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and…
The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in…
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…
A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th…
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian…
The generalised Wronskian of differential order $k\geqslant 1$ for $N$ functions $f_1$, $\ldots$, $f_N$ in $d\geqslant 1$ independent variables $x^1$, $\ldots$, $x^d$ is the determinant of the matrix with these functions' derivatives…
In this paper we prove generic results concerning Hardy spaces in one or several complex variables. More precisely, we show that the generic function in certain Hardy type spaces is totally unbounded and hence non-extentable, despite the…
In this paper, our main aim is to extend a classical theorem of Phelps on norm-attaining functionals from the space of scalar-valued continuous functions $C(\Omega)$ to its vector-valued counterpart $C(\Omega, X)$. One of our main results…
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…
This work presents a general principle, in the spirit of convex integration, leading to a method for the characterization of Young measures generated by gradients of maps in $W^{1,p}$ with $p$ less than the space dimension, whose Jacobian…
The relation between two Morse functions defined on a common domain can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the functions are aligned. Both the Jacobi set itself as…