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Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$ 1st ed. 2017 [Minkštas viršelis]

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  • Formatas: Paperback / softback, 155 pages, aukštis x plotis: 235x155 mm, VIII, 155 p., 1 Paperback / softback
  • Serija: Publications of the Scuola Normale Superiore 15
  • Išleidimo metai: 15-Feb-2017
  • Leidėjas: Scuola Normale Superiore
  • ISBN-10: 8876426000
  • ISBN-13: 9788876426001
Kitos knygos pagal šią temą:
Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$ 1st ed. 2017Didesnis paveikslėlis
  • Formatas: Paperback / softback, 155 pages, aukštis x plotis: 235x155 mm, VIII, 155 p., 1 Paperback / softback
  • Serija: Publications of the Scuola Normale Superiore 15
  • Išleidimo metai: 15-Feb-2017
  • Leidėjas: Scuola Normale Superiore
  • ISBN-10: 8876426000
  • ISBN-13: 9788876426001
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9788876426001.html
Raktažodžiai:
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.
Preface vii
1 Introduction
1(14)
1.1 The fractional Laplacian
1(5)
1.2 The mountain pass theorem
6(6)
1.3 The concentration-compactness principle
12(3)
2 The problem studied in this monograph
15(14)
2.1 Fractional critical problems
15(5)
2.2 An extended problem and statement of the main results
20(9)
3 Functional analytical setting
29(10)
3.1 Weighted Sobolev embeddings
29(6)
3.2 A concentration-compactness principle
35(4)
4 Existence of a minimal solution and proof of Theorem 2.2.2
39(28)
4.1 Some convergence results in view of Theorem 2.2.2
39(3)
4.2 Palais-Smale condition for Fε
42(23)
4.3 Proof of Theorem 2.2.2
65(2)
5 Regularity and positivity of the solution
67(8)
5.1 A regularity result
67(5)
5.2 A strong maximum principle and positivity of the solutions
72(3)
6 Existence of a second solution and proof of Theorem 2.2.4
75(74)
6.1 Existence of a local minimum for Jε
77(1)
6.2 Some preliminary lemmata towards the proof of Theorem 2.2.4
78(6)
6.3 Some convergence results in view of Theorem 2.2.4
84(6)
6.4 Palais-Smale condition for Jε
90(43)
6.5 Bound on the minimax value
133(15)
6.6 Proof of Theorem 2.2.4
148(1)
References 149