Dipierro, Serena. Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$ [electronic resource] / / by Serena Dipierro, María Medina, Enrico Valdinoci.. — 1st ed. 2017.. — VIII, 155 p. : online resource. — (Lecture Notes (Scuola Normale Superiore) ;) 15. - Lecture Notes (Scuola Normale Superiore) ; 15 .
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.
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Анотація: 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.
9788876426018
10.1007/978-88-7642-601-8 doi
Partial differential equations. Calculus of variations. Partial Differential Equations. Calculus of Variations and Optimal Control; Optimization.