1,721,103 research outputs found
Spectrum of the fractional p-Laplacian in RN and decay estimate for positive solutions of a Schrödinger equation
No full textIn this paper, we prove the existence of unbounded sequence of eigenvalues for the fractional p−Laplacian with weight in RN. We also show a nonexistence result when the weight has positive integral. In addition, we show some qualitative properties of the first eigenfunction including a sharp decay estimate. Finally, we extend the decay result to the positive solutions of a Schrödinger type equation.Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; ArgentinaFil: Quaas, Alexander. Universidad Técnica Federico Santa María; Chil
Global bifurcation for fractional p-Laplacian and an application
Full text linkWe prove the existence of an unbounded branch of solutions to the nonlinear non-local equation (Equation presented) bifurcating from the first eigenvalue. Here (-Δ)s p denotes the fractional p-Laplacian and Ω ⊂ ℝ1 is a bounded regular domain. The proof of the bifurcation results relies in computing the Leray-Schauder degree by making an homotopy respect to s (the order of the fractional p-Laplacian) and then to use results of local case (that is s = 1) found in the paper of del Pino and Manasevich [J. Diff. Equ. 92(1991) (2), 226-251]. Finally, we give some application to an existence result.Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Quaas, Alexander. Universidad Técnica Federico Santa María; Chil
A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian
Full text linkOur propose here is to provide a Hopf lemma and a strong minimum principle for weak supersolutions of (−Δp)su=c(x)|u|p−2u in Ω where Ω is an open set of RN, s∈(0,1), p∈(1,+∞), c∈C(Ω‾) and (−Δp)s is the fractional p-Laplacian.Fil: del Pezzo, Leandro Martin. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Quaas, Alexander. Universidad Técnica Federico Santa María; Chil
Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian
Full text linkIn this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional p-Laplacian. The first result is an existence in a non-resonant range more specific between the first and second eigenvalue of the fractional p-Laplacian. The second result is the anti-maximum principle for the fractional p-Laplacian.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Quaas, Alexander. Universidad Técnica Federico Santa María. Departamento de Matemática; Chil
A liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions
Full text linkIn this work we obtain a Liouville theorem for positive, bounded solutions of the equation where (-δ)s stands for the fractional Laplacian with s 2 (0; 1), and the functions h and f are nondecreasing. The main feature is that the function h changes sign in R, therefore the problem is sometimes termed as indefinite. As an application we obtain a priori bounds for positive solutions of some boundary value problems, which give existence of such solutions by means of bifurcation methods.Fil: Barrios, Begona. Universidad de La Laguna; EspañaFil: del Pezzo, Leandro Martin. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Garcia Melian, Jorge. Universidad de La Laguna; EspañaFil: Quaas, Alexander. Universidad Técnica Federico Santa María; Españ
Fractional convexity
Full text linkWe introduce a notion of fractional convexity that extends naturally the usual notion of convexity in the Euclidean space to a fractional setting. With this notion of fractional convexity, we study the fractional convex envelope inside a domain of an exterior datum (the largest possible fractional convex function inside the domain that is below the datum outside) and show that the fractional convex envelope is characterized as a viscosity solution to a non-local equation that is given by the infimum among all possible directions of the 1-dimensional fractional laplacian. For this equation we prove existence, uniqueness and a comparison principle (in the framework of viscosity solutions). In addition, we find that solutions to the equation for the convex envelope are related to solutions to the fractional Monge–Ampere equation.Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Quaas, Alexander. Universidad Técnica Federico Santa María; ChileFil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin
A priori bounds and existence of solutions for some nonlocal elliptic problems
Full text linkIn this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We obtain the a priori bounds by adapting the classical scaling method of Gidas and Spruck. We also deal with problems involving gradient terms.Fil: Barrios, Begoña. University of Texas at Austin; Estados UnidosFil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Garcia Melian, Jorge. Universidad de La Laguna; EspañaFil: Quaas, Alexander. Universidad Técnica Federico Santa María; Chil
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
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
- …
