186,244 research outputs found
Regularity results for p-Laplacians in pre-fractal domains
No full textWe study obstacle problems involving p-Laplace-type operators in non-convex polygons. We establish regularity results in terms of weighted Sobolev spaces. As applications, we obtain estimates for the FEM approximation for obstacle problems in pre-fractal Koch Islands
Regularity results for p-Laplacians in pre-fractal domains
No full textWe study obstacle problems involving p-Laplace-type operators in non-convex polygons. We establish regularity results in terms of weighted Sobolev spaces. As applications, we obtain estimates for the FEM approximation for obstacle problems in pre-fractal Koch Islands
Regularity and asymptotics for p-Laplace type operators in fractal and pre-fractal domains
No full textIn this thesis we deal with double obstacle problems involving p-Laplace type operators in fractal and pre-fractal domains of R^2.
The first improvement here presented consists in establishing a regularity result for the solution to double obstacle problem in terms of weighted Sobolev spaces (involving second derivatives), where we take as weight the distance from the vertex of the reentrant corner.
In particular, we prove local estimates, estimates far away from the conical point and the boundedness of the gradient far away from the conical point.
In addition, thanks to the regularity result presented, we establish a sharp error estimates for the FEM approximations follow the approach of P. Grisvard, considering a suitable triangulation of the domains, adapted to the regularity of the solutions. Furthermore, after stating this optimal estimate, we perform numerical simulations investigating both the cases of p = 2 and p > 2 (fixed).
In the last part of the work, considering both the case of fractal domains and the n-th pre-fractal ones, we investigate the asymptotic behaviour of the solution with respect to p and n. Moreover, we briefly discuss the issue of the uniqueness
Asymptotics for quasilinear obstacle problems in bad domains
No full textWe study two obstacle problems involving the p-Laplace operator in domains with n-th pre-fractal and fractal boundary. We perform asymptotic analysis for and
∞-Laplacian Obstacle Problems in Fractal Domains
No full textIn this paper we deal with p-Laplacian and ∞-Laplacian obstacle problems in fractal and pre-fractal domains, analyzing both the asymptotic behavior and the issue of the uniqueness of the solutions. Moreover, we consider numerical approximations, we state uniform estimates for FEM-approximate solutions and we discuss about the rate of vanishing of the approximation error
ANALYSIS OF THE MECHANISMS CONTROLLING THE EXPRESSION OF THE L1 RIBOSOMAL-PROTEIN GENE IN XENOPUS-LAEVIS
No full textIn vitro study of processing of the intron-encoded U16 small nucleolar RNA in Xenopus laevis
No full textIt was recently shown that a new class of small nuclear RNAs is encoded in introns of protein-coding genes and that they originate by processing of the pre-mRNA in which they are contained. Little is known about the mechanism and the factors involved in this new type of processing. The L1 ribosomal protein gene of Xenopus laevis is a well-suited system for studying this phenomenon: several different introns encode for two small nucleolar RNAs (snoRNAs; U16 and U18). In this paper, we analyzed the in vitro processing of these snoRNAs and showed that both are released from the pre-mRNA by a common mechanism: endonucleolytic cleavages convert the pre-mRNA into a precursor snoRNA with 5' and 3' trailer sequences. Subsequently, trimming converts the pre-snoRNAs into mature molecules. Oocyte and HeLa nuclear extracts are able to process X. laevis and human substrates in a similar manner, indicating that the processing of this class of snoRNAs relies on a common and evolutionarily conserved mechanism. In addition, we found that the cleavage activity is strongly enhanced in the presence of Mn2+ ions
Two different snoRNAs are encoded in introns of amphibian and human L1 ribosomal protein genes
No full textWe previously reported that the third intron of the X.laevis L1 ribosomal protein gene encodes for a snoRNA called U16. Here we show that four different introns of the same gene contain another previously uncharacterized snoRNA (U18) which is associated with fibrillarin in the nucleolus and which originates by processing of the pre-mRNA. The pathway of U18 RNA release from the pre-mRNA is the same as the one described for U16: primary endonucleolytic cleavages upstream and downstream of the U18 coding region produce a pre-U18 RNA which is subsequently trimmed to the mature form. Both the gene organization and processing of U18 are conserved in the corresponding genes of X.tropicalis and H.sapiens. The L1 gene thus has a composite structure, highly conserved in evolution, in which sequences coding for a ribosomal protein are intermingled with sequences coding for two different snoRNAs. The nucleolar localization of these different components suggests some common function on ribosome biosynthesis
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
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