1,721,004 research outputs found
A global existence result for a Keller-Segel type system with supercritical initial data
No full textOn the shape of blowup solutions to a mean field equation
No full textWe analyze the structure of non radial -point blow up solutions sequences for the Liouville type equation on the two dimensional unit disk,
-\lapl u(x)=\la \dfrac{\e{u(x)}}{\inb\e{u(x)} \dx}\;\;\mbox{in}\;\; D,
\;\;u(x)=0\;\;\mbox{on}\;\; D.
In case , we provide necessary and sufficient conditions for the existence of blow up solutions and, in the same spirit of \cite{cl1}, prove their axial symmetry with respect to the diameter joining the maximum points.
Finally, we prove that a non radial one point blow up solution exists only if \la-8\pi>0
Uniformly Elliptic Liouville Type Equations: Concentration Compactness and a Priori Estimates
No full textWe analyze the singular behavior of the Green's function for uniformly elliptic equations on smooth and bounded two dimensional domains. Then, we are able to generalize to the uniformly elliptic case some sharp estimates for Liouville type equations due to Brezis-Merle [7] and, in the same spirit of [3], a "mass" quantization result due to Y.Y. Li [21]. As a consequence, we obtain uniform a priori estimates for solutions of the corresponding Dirichlet problem. Then, we improve the standard existence theorem derived by direct minimization and, in the same spirit of [17] and [37], obtain the existence of Mountain Pass type solutions
Harnack type inequalities and quantization for the Uniformly Elliptic Liouville Equation
No full textWe extend the Harnack type inequality proved in C. R. Acad. Sci. Paris 315(2) (1992), 159-164, to the solutions of -div(A del u) = Ve(u) in Omega, with no boundary conditions. Here A is a symmetric, uniformly elliptic matrix and Omega subset of R-2 is open and bounded. As an application we are able to generalize the quantization results of Ind. Univ. Math. J. 43(4) (1994), 1255-1270, to the uniformly elliptic case
Blow up analysis, existence and qualitative properties of solutions for the two dimensional Emden-Fowler equation with singular potential
No full textMotivated by the study of a two-dimensional point vortex model, we analyze the following Emden-Fowler type problem with singular potential
\bgin{equation}\graf{
-\lapl u=\lm \dfrac{\e{u}}{\ino\e{u} \dx} & \mbox{in}\hspace{.2cm} \om,
\nonumber\\\\
\hspace{.55cm}u=0 & \hspace{-.05cm} \mbox{on}\hspace{.2cm} \om,
}\end{equation}
where \displaystyle V(x)=\frac{ K(x)}{|x|^{2\al}} with , 0< a\leq K(x)\leq b<+\infty, \fal{x}{\om} and \|\nabla K\|_\i\leq C.
We first extend various results, already known in case , to cover the case . In particular, we study the concentration-compactness problem and the mass quantization properties, obtaining some existence results.
Then, by a special choice of , we include the effect of the angular momentum in the system and obtain the existence of axially symmetric one peak non radial blow up solutions
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
Uniform Estimates and Blow-up Analysis for the Emden Exponential Equation in Any Dimension
No full textWe study the asymptotic behavior as n ->infinity of a sequence of functions u(n) satisfying the Emden equation Delta u(n) = e(un) in a bounded domain Omega subset of R-N, with N >= 2. By assuming a suitable uniform bound and an additional monotonicity property, we prove that the *-weak limit in the sense of measures of a subsequence of e(un) is either a function of L-1(Omega), or a purely singular measure concentrated on an (N - 2)-rectifiable set
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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