1,720,995 research outputs found
Uniqueness of solutions for an elliptic equation modeling MEMS
No full textWe show among other things, that for small voltage, the stable solution of the basic
nonlinear eigenvalue problem modelling a simple electrostatic MEMS is actually the unique solution,
provided the domain is star-shaped and the dimension is larger or equal than 3. In two dimensions,
we need the domain to be either strictly convex or symmetric. The case of a power permittivity
profile is also considered. Our results, which use an approach developed by Schaaf [13], extend and
simplify recent results by Guo and Wei [7], [8]
Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity
No full textWe study the branch of semistable and unstable solutions (i.e., those whose Morse index is at most 1) of the Dirichlet boundary value problem on a bounded domain , which models—among other things—a simple electrostatic microelectromechanical system (MEMS) device. We extend the results of [11] relating to the minimal branch, by obtaining compactness along unstable branches for 1 ≤ N ≤ 7 on any domain \Omega and for a large class of “permittivity profiles” f . We also show the remarkable fact that powerlike profiles f (x) ≃ |x|^α can push back the critical dimension N = 7 of this problem by establishing compactness for the semistable branch on the unit ball, also for N≥8 and as long as . As a byproduct, we are able to follow the second branch of the bifurcation diagram and prove the existence of a second solution for λ in a natural range. In all these results, the conditions on the space dimension and on the power of the profile are essentially sharp
Mathematical analysis of partial differential equations modeling electrostatic MEMS. COURANT LECTURE NOTES IN MATHEMATICS
No full textSign-changing solutions for critical equations with hardy potential
Full text linkWe consider the following perturbed critical Dirichlet problem involving the Hardy–Schrödinger operator: (Formula presented) when ε > 0 is small, (Formula presented), and where (Formula presented), N ≤ 3, is a smooth bounded domain with 0 ∈ Ω. We show that there exists a sequence (Formula presented) with (Formula presented) such that, if (Formula presented) for any j and (Formula presented), then the above equation has for ε small, a positive — in general nonminimizing — solution that develops a bubble at the origin. If moreover (Formula presented), then for any integer k ≤ 2, the equation has for small enough ε a sign-changing solution that develops into a superposition of k bubbles with alternating sign centered at the origin. The above result is optimal in the radial case, where the condition (Formula presented) is not necessary. Indeed, it is known that, if (Formula presented) and Ω is a ball B, then there is no radial positive solution for ε > 0 small. We complete the picture here by showing that, if (Formula presented), then the above problem has no radial sign-changing solutions for ε > 0 small. These results recover and improve what is already known in the nonsingular case, i.e., when γ = 0
The critical dimension for a fourth order elliptic problem with singular nonlinearity
No full textWe study the regularity of the extremal solution of the semilinear biharmonic equation \Delta^2 u = \frac{\lambda}{(1-u)^}, which models a simple micro-electromechanical system (MEMS) device on a ball , under Dirichlet boundary conditions on ∂B. We complete here the results of Lin and Yang [14] regarding the identification of a “pull-in voltage” such that a stable classical
solution with 1−C_0 |x|^{4/3}\leq u_λ∗(x)\leq 1 − |x|^{4/3}C 0= (λ∗/\bar λ)^{1/3} and
Regularity of extremal solutions in fourth order nonlinear eigenvalue problems on general domains
No full textWe examine the regularity of the extremal solution of the nonlinear eigenvalue problem on a general bounded domain in ,
with the Navier boundary condition on .
We establish energy estimates which show that for any non-decreasing convex and superlinear nonlinearity with , the extremal solution is smooth provided .
If in addition , then is regular for , while if , then the same holds for .
It follows that is smooth if and , or if and
.
We also show that if , and , then is smooth for . While these results are major improvements on what is known for general domains, they still fall short of the expected optimal results as recently established on radial domains, e.g., is smooth for when [J. Davila, L. Dupaigne, I. Guerra and M. Montenegro, Stable solutions for the bilaplacian with
exponential nonlinearity, SIAM J. Math. Anal., 39 (2007), 565–592], and for when [C. Cowan, P. Esposito, N. Ghoussoub and A. Moradifam, The critical dimension for a fourth
order elliptic problem with singular nonlinearity, Arch. Ration. Mech. Anal., 198 (2010), 763–787] (see also [A. Moradifam, On the critical dimension of a fourth order elliptic problem with negative exponent, J. Differential Equations, 248 (2010), 594–616]
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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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