1,720,988 research outputs found
Alcune note sulle funzioni di seminorma frazionaria Ws,1 minima
Full text linkIn this survey we discuss some existence and asymptotic results, originally obtained in [4,3], for functions of least Ws,1-fractional seminorm. We present the connection between these functions and nonlocal minimal surfaces, leveraging this relation to build a function of least fractional seminorm. We further prove that a function of least fractional seminorm is the limit for p → 1 of the sequence of minimizers of the Ws,p-energy. Additionally, we consider the fractional 1-Laplace operator and study the equivalence between weak solutions and functions of least fractional seminorm.In questa nota discutiamo alcuni risultati di esistenza e asintotici, originariamente ottenuti in [4,3], per le funzioni di seminorma frazionaria Ws,1 minima. Presentiamo la connessione tra queste funzioni e le superfici minime nonlocali, e ricorriamo a tale relazione per costruire una funzione di seminorma frazionaria minima. Otteniamo inoltre una funzione di seminorma frazionario minima come limite per p → 1 del minimo dell'energia frazionaria Ws,p. Consideriamo in più l'1-Laplaciano frazionario e mostriamo l'equivalenza tra le soluzioni deboli e le funzioni di seminorma frazionaria Ws,1 minima
Some observations on the Green function for the ball in the fractional Laplace framework
Full text linkWe consider a fractional Laplace equation and we give a selfcontained elementary exposition of the representation formula for the Green function on the ball. In this exposition, only elementary calculus techniques will be used, in particular, no probabilistic methods or computer assisted algebraic manipulations are needed. The main result in itself is not new, however we believe that the exposition is original and easy to follow, hence we hope that this paper will be accessible to a wide audience of young researchers and graduate students that want to approach the subject, and even to professors that would like to present a complete proof in a PhD or Master Degree cour
The stickiness phenomena of nonlocal minimal surfaces: new results and a comparison with the classical case
Full text linkWe discuss in this note the stickiness phenomena for nonlocal minimal surfaces. Classical minimal surfaces in convex domains do not stick to the boundary of the domain, hence examples of stickiness can be obtained only by removing the assumption of convexity. On the other hand, in the nonlocal framework, stickiness is ''generic''. We provide various examples from the literature, and focus on the case of complete stickiness in highly nonlocal regimes
Local density of Caputo-stationary functions in the space of smooth functions
Full text linkWe consider the Caputo fractional derivative and say that a function is Caputo-stationary if its Caputo derivative is zero. We then prove that any Ck( [ 0,1 ]) function can be approximated in [0,1] by a function that is Caputo-stationary in [0,1], with initial point a< 0. Otherwise said, Caputo-stationary functions are dense in Ckloc(R)
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Nonlocal diffusion and applications
Full text linkWorking in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Concavity principles for nonautonomous elliptic equations and applications
Full text linkIn the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming to get almost concavity results for a relevant class of anisotropic semilinear elliptic problems with spatially dependent source and diffusion
Potential theoretic approach to Schauder estimates for the fractional Laplacian
Full text linkWe present an elementary approach for the proof of Schauder estimates for the equation (-\Delta )^s u(x)=f(x), \,0<s<1, with having a modulus of continuity , based on the Poisson representation formula and dyadic ball approximation argument. We give the explicit modulus of continuity of in balls in terms of
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