1,720,960 research outputs found
The Hardy constant: a review
Full text linkWe present a review of results that have been obtained in the past
twenty-five years concerning the -Hardy inequality with distance to the
boundary. We concentrate on results where the best Hardy constant is either
computed exactly or estimated from below.Comment: 7 pages. To appear in the volume "Modern Problems in PDEs and
Applications - Extended Abstracts of the 2023 Ghent Analysis and PDE Center
Summer School", Research Perspectives Ghent Analysis and PDE Center, Trends
in Mathematics, Springer. Editors: M. Chatzakou, J. Restrepo, M. Ruzhansky,
B. Torebek, K. Van Bocksta
Spectral Theory of Singular Elliptic Operators with Measurable Coefficients
No full textAbstractWe study higher order elliptic operators with measurable coefficients acting on Euclidean domains. The coefficients may have degeneracies or singularities on the boundary or at infinity. We prove Gaussian-type bounds on the fundamental solution of the associated semigroup. These bounds are expressed in terms of a distanced(x, y) that reflects the singularity or degeneracy of the coefficients. The estimates are then used to extend the semigroup to otherLpspaces and to prove that theLp-spectrum isp-independent
Higher order linear parabolic equations
No full textWe first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the updated state of art and we suggest several open problems
Heat kernel estimates for fourth-order non-uniformly elliptic operators with non-strongly convex symbols
No full textWe obtain heat-kernel estimates for fourth-order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This entails certain difficulties as it is known that, as opposed to the strongly convex case, there is no absolute exponential constant. Our estimates involve sharp constants and Finsler-type distances that are induced by the operator symbol. The main result is based on two general hypotheses, a weighted Sobolev inequality and an interpolation inequality, which are related to the singularity or degeneracy of the coefficients.Mathematic
Heat kernel estimates for fourth order non-uniformly elliptic operators with non strongly convex symbols
No full textWe obtain heat kernel estimates for a class of fourth order non-uniformly
elliptic operators in two dimensions. Contrary to existing results, the
operators considered have symbols that are not strongly convex. This rises
certain difficulties as it is known that, as opposed to the strongly convex
case, there is no absolute exponential constant. Our estimates involve sharp
constants and Finsler-type distances that are induced by the operator symbol.
The main result is based on two general hypotheses, a weighted Sobolev
inequalitry and an interpolation inequality, which are related to the
singularity or degeneracy of the coefficients.Comment: 11 pages; minor correction
Monotonicity, continuity and differentiability results for the Lp Hardy constant
No full textWe consider the L^p Hardy inequality involving the distance to the boundary for a domain in the
n-dimensional Euclidean space. We study the dependence on p of the corresponding best constant and we prove monotonicity, continuity and differentiability results. The focus is on non-convex domains in which case such a constant is in general not explicitly known
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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