本文證明對∂－方程式在橢圓域中的解皆可用積分形式表現出來而且滿足均勻估計。在此估計中的常數可用橢圓的長短軸表達之。而且，我們也證明了此常數具有穩定性。 / In this thesis, we prove that, given any smooth closed (0,1)-form f near an ellipsoid Ω in Cⁿ, the Henkin's solution H_Ωf of the ∂-equation on Ω satisfies the uniform estimate 　　　　║H_Ωf║_∞≦C_Ω║f║_∞　　， 　　where is the Henkin's constant of Ω which can be explicitly estimated in terms of the maximum and minimum axes of the ellipsoid Ω. Also, a special version of the stability result of the Henkin's constant C_Ω is obtained.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-07-13T20:13:32Z No. of bitstreams: 2 Dissertação - Mauricio Silva Louzeiro - 2016.pdf: 1453255 bytes, checksum: c23898f8b30d7250d9fc245034078281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-07-14T13:28:30Z (GMT) No. of bitstreams: 2 Dissertação - Mauricio Silva Louzeiro - 2016.pdf: 1453255 bytes, checksum: c23898f8b30d7250d9fc245034078281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-07-14T13:28:30Z (GMT). No. of bitstreams: 2 Dissertação - Mauricio Silva Louzeiro - 2016.pdf: 1453255 bytes, checksum: c23898f8b30d7250d9fc245034078281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we will study a new strategy to minimize a convex function on a simplicial cone. This method consists in to obtain the solution of a minimization problem through the root of a semi-smooth equation associated to its optimality conditions. To nd this root, we use the semi-smooth version of the Newton's method, where the derivative of the function that de nes the semi-smooth equation is replaced by a convenient Clarke subgradient. For the case that the function is quadratic, we will see that it allows us to have weaker conditions for the convergence of the sequence generated by the semi-smooth Newton's method. Motivated by this new minimization strategy we will also use the semi-smooth Newton's method to nd roots of two special semi-smooth equations, one associated to x+ and the another one associated to jxj. / Neste trabalho, estudaremos uma nova estrat egia para minimizar uma fun c~ao convexa sobre um cone simplicial. Este m etodo consiste em obter a solu c~ao do problema de minimiza c~ao atrav es da raiz de uma equa c~ao semi-suave associada as suas condi c~oes de otimalidade. Para encontrar essa raiz, usaremos uma vers~ao semi-suave do m etodo de Newton, onde a derivada da fun c~ao que de ne a equa c~ao semi-suave e substitu da por um subgradiente de Clarke conveniente. Para o caso em que a fun c~ao e quadr atica, veremos que e poss vel obter condi c~oes mais fracas para a converg^encia da sequ^encia gerada pelo m etodo de Newton semi-suave. Motivados por esta nova estrat egia de minimiza c~ao tamb em usaremos o m etodo de Newton semi-suave para encontrar ra zes de dois tipos espec cos de equa c~oes semi-suaves, uma associada a x+ e a outra associada a jxj.