I dedicate this thesis to everyone who realised that self-knowledge is a person's truest possession and a most valued treasure. Besides my advisor, I would like to thank Prof. Thierry Barbot, who supervised me during my stay in France, for his encouragement, hard questions and immense knowledge. My sincere thanks to all my professors, who taught, guided and helped me during this part of the never ending journey of learning. In particular I thank Prof. Carlos Grossi and Prof. Sasha Ananin who helped me to broaden my horizons with respect to mathematics and look at areas beyond my own. I thank my family, for their continuous, unwavering and unconditional support, for their love and patience through the whole process of my PhD.
Denição 2.1. Seja P (D) um operador com coecientes constantes. Um conjunto Ω ⊂ R n é dito P -convexo para suporte se para todo compacto K ⊂ Ω existe um outro compactoDizemos que Ω é P -convexo para suporte singular se para todoOs seguintes resultados se encontram em Hörmander [2005] e sua referência se encontra entre parênteses. Teorema 2.2 (Corolario 10.7.10). A equação P (D)u = f possui solução u ∈ D ′ (Ω) para todo f ∈ D ′
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