Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$ [electronic resource] /
Dipierro, Serena.author.
Medina, María.author.
Valdinoci, Enrico.author.
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 original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.
Includes bibliographical references.
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.
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 original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.
Partial differential equations.
Calculus of variations.
Partial Differential Equations.
Calculus of Variations and Optimal Control; Optimization.