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Let Ω⊂Cn be a bounded starlike circular domain with 0∈Ω. In this paper, we introduce a class of holomorphic mappings Mg on Ω. Let f(z) be a normalized locally biholomorphic mapping on Ω such that and z=0 is the zero of order k+1 of f(z)−z. We obtain a sharp growth theorem and sharp coefficient bounds for f(z). As applications, sharp distortion theorems for a subclass of starlike mappings are obtained. These results unify and generalize many known results. 相似文献
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Elder Jesús Villamizar-Roa María Ángeles Rodríguez-Bellido Marko Antonio Rojas-Medar 《数学学报(英文版)》2010,26(5):837-862
Assuming that the external forces of the system are small enough, the reference temperature being a periodic function, we study the existence, the uniqueness and the regularity of time-periodic solutions for the Boussinesq equations in several classes of unbounded domains of Rn. Our analysis is based on the framework of weak-Lp spaces. 相似文献
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Martin Schechter 《Journal of Mathematical Analysis and Applications》2007,327(2):1143-1154
As formulated by Silva [E.A. de B.e. Silva, Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Anal. 16 (1991) 455-477] and Schechter [M. Schechter, A generalization of the saddle point method with applications, Ann. Polon. Math. 57 (3) (1992) 269-281; M. Schechter, New saddle point theorems, in: Generalized Functions and Their Applications, Varanasi, 1991, Plenum, New York, 1993, pp. 213-219], the sandwich theorem has become a very useful tool in finding critical points of functionals leading to solutions of partial differential equations. In the present paper, this theorem is strengthened to apply to more general situations. We present some applications. 相似文献
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J. A. S. Martins 《Annali di Matematica Pura ed Applicata》1977,115(1):271-294
Summary Piecewise polynomial and Fourier approximation of functions in the Sobolev spaces
on unbounded domains Θ ⊂ Rn are applied to the study of the type of compact embeddings into appropriate Lebesgue and Orlicz spaces. It is shown that
if Θ and s satisfy certain conditions, the embeddings
, m/n+1/q−1/p>0 and
, Φ being an Orlicz function subordinate to both φ(t)=|t|p
exp |t|n/(n−m) and Φσ(t)=exp |t|σ−1, σ ⩾ 1, m/n>1/p, are of type ls. One result dealing with multiplications maps from
into Lq(Θ) is also obtained.
Entrata in Redazione il 14 ottobre 1976. 相似文献
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We prove several existence and non-existence results for a quasilinear eigenvalue problem with nonlinear boundary condition on unbounded domain. Our paper extends previous results obtained in Chabrowski [1] and Pflüger [4]. 相似文献
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Two graphs are said to be A-cospectral if they have the same adjacency spectrum. A graph G is said to be determined by its adjacency spectrum if there is no other non-isomorphic graph A-cospectral with G. A tree is called starlike if it has exactly one vertex of degree greater than 2. In this article, we prove that the line graphs of starlike trees with maximum degree at least 12 are determined by their adjacency spectra. 相似文献
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Jorge Buescu 《Journal of Mathematical Analysis and Applications》2004,296(1):244-255
We study positive integral operators in with continuous kernel k(x,y). We show that if the operator is compact and Hilbert-Schmidt. If in addition k(x,x)→0 as |x|→∞, k is represented by an absolutely and uniformly convergent bilinear series of uniformly continuous eigenfunctions and is trace class. Replacing the first assumption by the stronger then and the bilinear series converges also in L1. Sharp norm bounds are obtained and Mercer's theorem is derived as a special case. 相似文献
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Dedicated to Professor Hiroki Tanabe on the occasion of his sixtieth birthday 相似文献
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Jorge Mujica Paula Takatsuka 《Proceedings of the American Mathematical Society》2007,135(4):1141-1144
We show that if is a starlike domain in a Banach space and is a family of holomorphic functions on that omit two distinct values and is bounded at the origin, then is uniformly bounded on each -bounded set.
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Laurence Halpern. 《Mathematics of Computation》1996,65(214):507-531
We present spectral methods for solving the Stokes problem in a circular domain. Their main feature is the uniform inf-sup condition, which allows for optimal error estimates. We apply them to the resolution of exterior problems by coupling with the transparent boundary condition.
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Sofia Melo 《Bulletin of the Brazilian Mathematical Society》2014,45(1):91-116
We study the existence of minimal graphs in with prescribed boundary data, possibly infinite. We give necessary and sufficient conditions on the “lengths” of the sides of the inscribed polygons in an unbounded domain in ?2, that yield solutions to the minimal surface equation with prescribed boundary data. 相似文献
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Summary The time dependent dam problem in a general unbounded domain is studied and an existence theorem is proved by means of a rather general approximation procedure. Moreover the propagation of the support of the solution is studied in a number of geometrical situations of interest. The corresponding stationary problem is also studied and an existence theorem is proved. Finally several one-dimensional examples are given in which the solution can be either written explicitely or found solving an ordinary differential equation.This work has been supported by MURST (Italy), by I.A.N.-C.N.R. of Pavia (Italy), and by SFB 123 of University of Heidelberg (Germany). 相似文献
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Mohan Namasivayam 《Annali di Matematica Pura ed Applicata》1986,144(1):157-172
Summary
Integral representations of junctions in the anisotropic Sobolev spaces
on unbounded domains are used in the study of the embeddings of these spaces into Lebesgue spaces. Estimates of entropy numbers of the embedding
are obtained, where k, p and q satisfy certain conditions and where is a certain type of quasibounded domain, 相似文献