Fractional Elliptic Problems with Critical Growth in the Whole of ℝn

• Main Authors: Dipierro, Serena (Author), Medina, María (Author), Valdinoci, Enrico (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2017.
• Series: Publications of the Scuola Normale Superiore ; 15
• Subjects: Mathematics.; Partial differential equations.; Calculus of variations.; Partial Differential Equations.; Calculus of Variations and Optimal Control; Optimization.

These lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are o...

Table of Contents:

• Introduction
• The problem studied in this monograph
• Functional analytical setting
• Existence of a minimal solution and proof of Theorem 2.2.2
• Regularity and positivity of the solution
• Existence of a second solution and proof of Theorem 2.2.4.