1,391 research outputs found
Characterization by Asymptotic Mean Formulas of q−Harmonic Functions in Carnot Groups
No full textAim of this paper is to extend the work (Ferrari et al. in Discrete Contin. Dyn. Syst. 34, 2779–2793, 2014) to the Carnot group setting. More precisely, we prove that in every Carnot group a function is q−harmonic (here 1 < q < ∞), if and only if it satisfies a particular asymptotic mean value formula
Preface to Proceedings of the workshop "Something about nonlinear problems" held in Bologna, Italy, June 13-14, 2019.
No full textPrefazion
Some counterexamples to Alt–Caffarelli–Friedman monotonicity formulas in Carnot groups
Get PDFIn this paper we continue the analysis of an Alt-Caffarelli-Friedman (ACF) monotonicity formula in Carnot groups of step s >1 confirming the existence of counterexamples to the monotone increasing behavior. In particular, we provide a sufficient condition that implies the existence of some counterexamples to the monotone increasing behavior of the ACF formula in Carnot groups.
The main tool is based on the lack of orthogonality of harmonic polynomials in Carnot groups. This paper generalizes the results proved in n Ferrari and Forcillo (Atti Accad
Naz Lincei Rend Lincei Mat Appl 34(2):295–306, 2023)
Preface: Glimpses of a Metamorphic Scenario
No full textQuesto saggio costituisce il testo della Prefazione alla sezione di Cultura negli Atti del XXVIII Convegno AIA (Associazione Italiana di Anglistica), svoltosi presso l’Università di Pisa nei giorni 14-16 settembre 2017. La Prefazione, scritta da Laura Giovannelli e Fausto Ciompi, intende far luce su alcuni assunti teorici fondamentali e sviluppi recenti legati ai Cultural Studies, fornendo anche una panoramica dei dodici saggi raccolti nella parte dedicata al workshop di Cultura. Tra gli ambiti e le questioni di interesse figurano il trauma e il tema dell’identità etnica, la globalizzazione e il cyberspazio, la politica dell’intermedialità e i pattern comunicativi nell’universo dei social network. Viene così delineata una ricca cartografia nella quale i paradigmi di complessità, creatività e convenzionalità sono investigati in rapporto ai rispettivi e rilevanti contesti situazionali.This essay constitutes the Preface to the Culture-Section Proceedings of the 28th biennial Conference of the Italian Association of English Studies (AIA), which was held in Pisa on 14-16 September 2017. Written by Laura Giovannelli and Fausto Ciompi, this Preface intends to throw light on some pivotal theoretical assumptions and latest developments relating to Cultural Studies and it also provides a critical survey of the twelve papers collected here. Attention is paid to a variety of issues and fields such as trauma and ethnicity, globalisation and cyberspace, the politics of intermediality and communication patterns in social networks. A rich cartography is thus drawn in which the paradigms of complexity, creativity and conventionality are investigated in connection with their most relevant material contexts
Weyl and Marchaud Derivatives: A Forgotten History
Get PDFIn this paper, we recall the contribution given by Hermann Weyl and André Marchaud to the notion of fractional derivative. In addition, we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics
Some Nonlocal Operators in the First Heisenberg Group
Get PDFIn this paper we construct some nonlocal operators in the Heisenberg group. Specifically, starting from the Grünwald-Letnikov derivative and Marchaud derivative in the Euclidean setting, we revisit those definitions with respect to the one of the fractional Laplace operator. Then, we define some nonlocal operators in the non-commutative structure of the first Heisenberg group adapting the approach applied in the Euclidean case to the new framework
Fourier TransformEncyclopedia of Thermal Stresses
No full textThe Fourier transform is a key tool in several research fields: engineering, mathematics, applied mathematics, and physical science. We approach to this instrument assuming that the mathematical background of the readers might be various. Hence, the subject has been developed progressively. In particular in the first vintroductory part, the main relationship with the Fourier series has been put in evidence. Successively a rigorous mathematical discussion permits to deal with the subject in different functional spaces even arriving to the distributional framework. Some examples and applications are vintroduced and developed in the detail. In order to give the larger spectrum concerning the Fourier transform applications, even some topics like the discrete Fourier transform and the Shannon theorem are discussed
Mean value properties of fractional second order operators
No full textIn this paper we introduce a method to define fractional operators using mean value operators. In particular we discuss a geometric approach in order to construct fractional operators. As a byproduct we define fractional linear operators in Carnot groups, moreover we adapt our technique to define some nonlinear fractional operators associated with the p−Laplace operators in Carnot groups
Regolarità delle soluzioni viscose per equazioni a derivate parziali non lineari degeneri
No full textScopo di questa ricerca è lo studio delle proprietà di regolarità
delle soluzioni viscose di equazioni a derivate parziali non lineari
degeneri
Some a priori estimates for a class of operators in the Heisenberg group
No full textIn this note, we provide some a priori estimates for a class of operators that stem from the Laplacian in the Heisenberg group. We follow the idea contained in a proof given by Talenti, see (Ann Scuola Norm Sup Pisa Cl Sci (4) 3(4): 697–718, 1976), by adapting the classical notion of symmetrized rearrangement of a function to the framework of the Heisenberg group
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