On some elliptic problems involving powers of the Laplace operator

This PhD Thesis is devoted to the study of some elliptic problems involving powers of the positive Laplace operator This Doctoral Thesis has been supported by a PIPF Grant from Departamento de Matemáticas of Universidad Carlos III de Madrid. Additionally, the author has been partially supported by the Ministry of Economy and Competitiveness of Spain and FEDER under Research Project MTM2016-80618-P. Programa Oficial de Doctorado en Ingeniería Matemática Presidente: José Manuel Rodríguez García.- Secretario: Jesús García Azorero.- Vocal: Antonio Suárez Fernández