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Some properties of solutions to weakly hypoelliptic equationsBär, Christian January 2012 (has links)
A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which covers all elliptic, overdetermined elliptic, subelliptic and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients we show that Liouville's theorem holds, any bounded solution must be constant and any L^p solution must vanish.
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Dinâmica de endomorfismos do plano complexo e conjuntos de Julia na esfera de RiemanMarchioli, Andresa Baldam [UNESP] 10 August 2009 (has links) (PDF)
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marchioli_ab_me_sjrp.pdf: 317494 bytes, checksum: 518683b62d488d3433a0bee79ecd4f53 (MD5) / Neste trabalho, estudaremos as propriedades dinâmicas de endomorfismos do plano complexo C. Provaremos e o teorema de Montel e mostraremos algumas propriedades topológicas do conjunto de Julia J(f), onde f : C seta C é uma aplicação racional de grau > ou = 2 / In this work, we will study the dynamical properties of endomorfisms of complex plane C. We will also prove Montel's theorem and show some topological properties of Julia set J(f), where f : C 'seta' C is a rational map of degree > ou = 2.
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