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1	∂－方程解之積分表現及其在橢圓域之均勻估計 / Integral Representation of Solution for ∂u=f and Its Uniform Estimate on Ellipsoids 林景隆, Lin, Jin Long Unknown Date (has links) 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 C<sup>n</sup>, the Henkin's solution H<sub>Ω</sub>f of the ∂-equation on Ω satisfies the uniform estimate 　　　　║H<sub>Ω</sub>f║<sub>∞</sub>≦C<sub>Ω</sub>║f║<sub>∞</sub>　　，　　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<sub>Ω</sub> is obtained. 半凸集橢圓域平滑方程式長軸穩定性 pseudoconvex ellipsoid smooth-equation maximum axes stability