1,720,984 research outputs found
A Carleson-type estimate in Lipschitz type domains for non-negative solutions to Kolmogorov operators
Full text linkWe prove bondary Harnack estimates, in Lipschitz domains, for non-negative solutions to a class of second order degenerate dierential operators of Kolmogorov type. Our estimate is scale-invariant and generalizes previous results, valid for second order uniformly parabolic equations, to the class of operators considered
A note on Harnack inequalities and propagation set for a class of hypoelliptic operators
Full text linkIn this paper we are concerned with Harnack inequalities for non-negative solutions to a class of second order hypoelliptic ultraparabolic partial differential equations in the form
where the vector fields and are invariant with respect to a suitable homogeneous Lie group on .
Our main goal is the following result: consider any domain of and fix any in . We give a geometric sufficient condition on the compact subsets of for which the Harnack inequality
holds for all non-negative solutions to the equation in .
We also compare our result with an abstract Harnack inequality from potential theory
A Boundary Harnack Inequality for Singular Equations of p-Parabolic Type
Full text linkWe prove a boundary Harnack type inequality for nonnegative solutions to singular equations of p-parabolic type, 2n/(n+1)<p<2, in a time-independent cylinder whose base is C1,1-regular. Simple examples show, using the corresponding estimates valid for the heat equation as a point of reference, that this type of inequality cannot, in general, be expected to hold in the degenerate case ( 2<p<∞)
Regularity near the Initial State in the Obstacle Problem for a class of Hypoelliptic Ultraparabolic Operators
Full text linkThis paper is devoted to a proof of regularity, near the initial state, for solutions to the Cauchy-Dirichlet and obstacle problem for a class of second order differential operators of Kolmogorov type. The approach used here is general enough to allow us to consider smooth obstacles
as well as non-smooth obstacles
A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form
No full textWe consider non-negative solutions to a class of second-order degenerate Kolmogorov operators of the form \fancyscriptL=∑i,j=1mai,j(z)∂xixj+∑i=1mai(z)∂xi+∑i,j=1Nbi,jxi∂xj−∂t, where z = (x, t) belongs to an open set Ω⊂RN×R , and 1 ≤ m ≤ N. Let z˜∈Ω , let K be a compact subset of Ω−− , and let Σ⊂∂Ω be such that K∩∂Ω⊂Σ . We give sufficient geometric conditions for the validity of the following Carleson type estimate. There exists a positive constant C K , depending only on Ω,Σ,K,z˜ and on \fancyscriptL , such that supKu≤CKu(z˜), for every non-negative solution u of \fancyscriptLu=0 in Ω such that u∣Σ=0
Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets
Full text linkIn this paper we prove, by showing that solutions have exactly the same degree of regularity as the obstacle, optimal regularity results for obstacle problems involving evolutionary p-Laplace type operators. A main ingredient, of independent interest, is a new intrinsic interpolative geometry allowing for optimal linearization principles via blow-up analysis at contact points. This also opens the way to the proof of a removability theorem for solutions to evolutionary p-Laplace type equations. A basic feature of the paper is that no differentiability in time is assumed on the obstacle; this is in line with the corresponding linear results
Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options
Full text linkIn this paper we prove optimal interior regularity for solutions to the obstacle problem for a class of second order differential operators of Kolmogorov type. We treat smooth obstacles as well as non-smooth obstacles. All our proofs follow the same line of thought and are based on blow-ups, compactness, barriers and arguments by contradiction. This problem arises in financial mathematics, when considering path-dependent derivative contracts with the early exercise feature
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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