Related papers: Sign Changing Critical Points for Locally Lipschit…

In the paper we introduce Orlicz type functional spaces defined in terms of nonlocal convolution type integral functionals and study the main properties of these spaces. We show in particular that, under natural convexity and growth…

Our main result concerns the following condition: {\bf Condition C.} Let $X$ be a Banach space. A $C^1$ function $f:X\rightarrow \mathbb{R}$ satisfies Condition C if whenever $\{x_n\}$ weakly converges to $x$ and $\lim…

We solve some open problems regarding diameter two properties within the class of Banach spaces of real-valued Lipschitz functions by using the de Leeuw transform. Namely, we show that: the diameter two property, the strong diameter two…

The question of extension of locally defined maps to the entire space arises in many problems of analysis (e.g., local linearization of functional equations). A known classical method of extension of smooth local maps on Banach spaces uses…

Recently, samplets have been introduced as localized discrete signed measures which are tailored to an underlying data set. Samplets exhibit vanishing moments, i.e., their measure integrals vanish for all polynomials up to a certain degree,…

We have previously developed a polymer-like expansion that applies when the (effective) action in a functional integral is an analytic function of the fields being integrated. Here, we develop methods to aid the application of this…

We study local minima of the $p$-conformal energy functionals, \[ \mathsf{E}_{\cal A}^\ast(h):=\int_\ID {\cal A}(\IK(w,h)) \;J(w,h) \; dw,\quad h|_\IS=h_0|_\IS, \] defined for self mappings $h:\ID\to\ID$ with finite distortion of the unit…

We comment on a recent letter by L. C. de Albuquerque and M. M. Leite (J. Phys. A: Math. Gen. 34 (2001) L327-L332), in which results to second order in $\epsilon=4-d+\frac{m}{2}$ were presented for the critical exponents…

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to…

Recently there has been interest in pairs of Banach spaces $(E_0,E)$ in an $o-O$ relation and with $E_0^{**}=E$. It is known that this can be done for Lipschitz spaces on suitable metric spaces. In this paper we consider the case of a…

We consider integral functionals with slow growth and explicit dependence on u of the lagrangian; this includes many relevant examples, as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to…

A fixed point result is given for a class of functional contractions over local Branciari metric spaces. It extends some contributions in the area due to Fora et al [Mat. Vesnik, 61 (2009), 203-208].

We study the structure of the space of coarse Lipschitz maps between Banach spaces. In particular we introduce the notion of norm attaining coarse Lipschitz maps. We extend to the case of norm attaining coarse Lipschitz equivalences, a…

For $\sigma>0$, the Bernstein space \ $B^1_{\sigma}$ consists of those $L^1(R)$\ functions whose Fourier transforms are supported by $[-\sigma,\sigma]$. Since $B^1_{\sigma}$ is separable and dual to some Banach space, the closed unit ball…

We study a $p$-Laplacian equation involving a parameter $\lambda$ and a concave-convex nonlinearity containing a weight which can change sign. By using the Nehari manifold and the fibering method, we show the existence of two positive…

In this paper we investigate the nature of stationary points of functionals on the space of Riemannian metrics on a smooth compact manifold. Special cases are spectral invariants associated with Laplace or Dirac operators such as functional…

It is established the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional laplacian, nonlinearities with critical exponential growth and potentials this is which may change sign. The…

It was established in [8] that Lipschitz inf-compact functions are uniquely determined by their local slope and critical values. Compactness played a paramount role in this result, ensuring in particular the existence of critical points. We…

Motivated by the question of Mikael de la Salle, we investigate the problem of the existence of equivalent strictly convex norms on Banach spaces that are invariant with respect to an action of a group by linear isometries. We develop…

We obtain some new characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of sharp maximal functions, fractional maximal functions or fractional maximal commutators in the context of the…