1,720,991 research outputs found
Local minimizers in absence of ground states for the critical NLS energy on metric graphs
Full text linkWe consider the mass-critical non-linear Schrödinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to global minimizers of the energy functional under a mass constraint, is provided by Adami, Serra and Tilli in [R. Adami, E. Serra and P. Tilli. Negative energy ground states for the L2-critical NLSE on metric graphs. Comm. Math. Phys. 352 (2017), 387-406.], where it is proved that existence and properties of ground states depend in a crucial way on both the value of the mass, and the topological properties of the underlying graph. In this paper we address cases when ground states do not exist and show that, under suitable assumptions, constrained local minimizers of the energy do exist. This result paves the way to the existence of stable solutions in the time-dependent equation in cases where the ground state energy level is not achieved
Normalized solutions for Sobolev critical Schrödinger equations on bounded domains
No full textWe study the existence and multiplicity of positive solutions with prescribed L2norm for the Sobolev critical Schróodinger equation on a bounded domain \Omega \subset \BbbRN, N \geq 3,-\DeltaU = \lambdaU + U2\ast-1, U \in H01(\Omega), \int\Omega U2 dx = \rho2, where 2\ast = N2-N2 . First, we consider a general bounded domain \Omega in dimension N \geq 3, with a restriction, only in dimension N = 3, involving its inradius and first Dirichlet eigenvalue. In this general case, we show the existence of a mountain pass solution on the L2-sphere for \rho belonging to a subset of positive measure of the interval (0, \rho\ast\ast) and for a suitable threshold \rho\ast\ast > 0. Next, assuming that \Omega is star-shaped, we extend the previous result to all values \rho \in (0, \rho\ast\ast). With respect to that of local minimizers, already known in the literature, the existence of mountain pass solutions in the Sobolev critical case is much more elusive. In particular, our proofs are based on the sharp analysis of the bounded Palais-Smale sequences, provided by a nonstandard adaptation of the Struwe monotonicity trick that we develop
Solvability of a plane elliptic problem for the flow in a channel with a surface-piercing obstacle
Full text linkLet us consider the three-dimensional problem of the steady flow of a heavy ideal fluid past a surface-piercing obstacle in a rectangular channel of constant depth. The flow is parallel at infinity upstream, with constant velocity c. We discuss an approximate linear problem obtained in the limit of a "flat obstacle". This is a boundary value problem for the Laplace equation in a three-dimensional unbounded domain, with a second order condition on part of the boundary, the Neumann-Kelvin condition. By a Fourier expansion of the potential function, we reduce the three-dimensional problem to a sequence of plane problems for the Fourier coefficients; for every value of the velocity c, these problems can be described in terms of a two parameter elliptic problem in a strip. We discuss the two dimensional problem by a special variational approach, relying on some a priori properties of finite energy solutions; as a result, we prove unique solvability for 〖c≠c〗_(m,k) where c_(m,k) is a known sequence of values depending on the dimensions of the channel and on the limit length of the obstacle. Accordingly, we can prove the existence of a solution of the three-dimensional problem; the related flow has in general a non trivial wave pattern at infinity downstream. We also investigate the regularity of the solution in a neighborhood of the obstacle. The meaning of the singular values c_(m,k) is discussed from the point of view of the nonlinear theory
Concentration along geodesics for a nonlinear Steklov problem arising in corrosion modeling
No full textWe consider the problem of finding pairs (λ, u), with λ > 0 and u a harmonic function in a three-dimensional torus-like domain D, satisfying the nonlinear boundary condition ∂νu = λ sinh u on ∂D. This type of boundary condition arises in corrosion modeling (Butler-Volmer condition). We prove the existence of solutions which concentrate along some geodesics of the boundary ∂D as the parameter λ goes to zero
A system for off-line analysis of left ventricular angiographic images by the use of a minicomputer
No full textOn the Reconstruction of Cavities in a Nonlinear Model Arising from Cardiac Electrophysiology
Full text linkIn this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac electrophysiology. Based on the results obtained in [9] we propose a new reconstruction algorithm based on Gamma-convergence. The relevance and applicability of this approach are then shown through several numerical experiments
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
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