Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions

We introduce an iterative method for computing the first eigenpair $(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet data as the limit of $(\mu_{q,}u_{q})$ as $q\rightarrow p^{-}$, where $u_{q}$ is the positive solution of the sublinear Lane-Emden equation $-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of $u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of $\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence is presented.Comment: Section 5 was rewritten. Jed Brown was added as autho

Limits for Monge-Kantorovich mass transport problems

In this paper we study the limit of Monge-Kantorovich mass transfer problems when the involved measures are supported in a small strip near the boundary of a bounded smooth domain, Ω. Given two absolutely continues measures (with respect to the surface measure) supported on the boundary ∂Ω, by performing a suitable extension of the measures to a strip of width ε near the boundary of the domain Ω we consider the mass transfer problem for the extensions. Then we study the limit as ε goes to zero of the Kantorovich potentials for the extensions and obtain that it coincides with a solution of the original mass transfer problem. Moreover we look for the possible approximations of these problems by solutions to equations involving the p-Laplacian for large values of p.Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Reproductive biology of the dusky grouper Epinephelus marginatus (Lowe, 1834) (Perciformes: Serranidae, Epinephelinae) in Santa Catarina, Brazil

Copyright © 2003 Tecpar.Este trabalho trata sobre a biologia reprodutiva da garoupa verdadeira, Epinephelus marginatus (Lowe, 1834) um peixe teleósteo pertencente à família Serranidae, hermafrodita protogínico e característico do litoral rochoso, que vive desde águas rasas até os 200 m de profundidade. As amostragens foram realizadas nas ilhas que compõem a Reserva Biológica Marinha do Arvoredo (SC) e ilhas costeiras próximas da região de Florianópolis entre março de 1998 e maio de 2000. Dados de coletas de juvenis em poças de marés foram utilizados visando relacionar a sua ocorrência nestes ambientes com o período de pós-reprodução. Procedeu-se à análise histológica de 109 exemplares, a partir da qual foram descritas as alterações histológicas nas gônadas ao longo do seu ciclo sexual e foram estabelecidas as escalas de maturação. Desta forma determinou-se um tamanho de primeira maturação para as fêmeas (Lº=470 mm; r²=0,99). O comportamento dos valores dos índices calculados (Índice Hepatossomático (IHS) e Índice Gonadossomático (IGS)) elucidou um período reprodutivo com maturação das gônadas ao longo dos meses de primavera, vindo a desovar na estação do verão, sendo nítida a recuperação do fígado (elevação do IHS) no outono, pós reprodução. Calculou-se também a relação peso comprimento P = 9 • 10ˉ6 • TL3.1149 (r²=0.998; n=246).ABSTRACT: Investigations were carried out about the reproductive biology of the dusky grouper, Epinephelus marginatus (Lowe, 1834) a serranid protogynous hermaphrodite fish inhabitant of rocky bottoms from shallow waters up to 200 m depth. Samples were caught in the islands that form Arvoredo Biological Marine Reserve (SC - Brazil) and the coastal islands near Florianópolis region from March 1998 to May 2000. Data from samples of juvenile groupers on intertidal pools were used to link their occurrence in the pools to the post-spawning season. To describe the histological changes on gonads along the reproductive cycle and to establish maturation scales, 109 groupers were histologically tested for sex determination. First maturation size was determined for females (Lº=470 mm; r²=0.99). The results of calculated gonadosomatic (GSI) and hepatosomatic (HSI) indexes showed that maturation occurred along the spring months and the spawning activity during the summer with a peak in December. Liver recovery (HSI elevation) was evident in the autumn, was the post spawning season. The relationship between length and weight was W = 9 • 10ˉ6 • TL3.1149 (r²=0.998; n=246)