On some nonlocal elliptic problems

• Autores: Urko Sanchez Sanz
• Directores de la Tesis: Eduardo Colorado Heras (dir. tes.) , Arturo de Pablo (dir. tes.)
• Lectura: En la Universidad Carlos III de Madrid ( España ) en 2014
• Idioma: inglés
• Tribunal Calificador de la Tesis: José María Arrieta Algarra (presid.) , José Manuel Rodríguez García (secret.) , Ana Rodríguez Santamaría (voc.)
• Enlaces
  • Tesis en acceso abierto en: e-Archivo
• Resumen

  • This work is devoted to study some nonlocal elliptic problems involving the so-called fractional Laplacian, $(-\Delta)^{\alpha/2}$. In order to deal with these problems, several classical methods and techniques have been generalized to our context. Among these techniques we include the moving planes method, concentration compactness principle and a Pohozaev-type equation. This work is divided as follows:

    - Chapter 1: Introduction to the fractional Laplacian operator.

    - Chapter 2: A concave-convex elliptic problem involving the fractional Laplacian - Chapter 3: On some critical problems for the fractional Laplacian operator - Chapter 4: Perturbations of a critical fractional equation