NDLI: The Brezis–Nirenberg problem for the fractional p-Laplacian

Content Provider	SpringerLink
Author	Perera, Kanishka Squassina, Marco Mosconi, Sunra Yang, Yang
Copyright Year	2016
Abstract	We obtain nontrivial solutions to the Brezis–Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when $$p \ne 2$$ . We get around this difficulty by working with certain asymptotic estimates for minimizers recently obtained in (Brasco et al., Cal. Var. Partial Differ Equations 55:23, 2016). The second difficulty is the lack of a direct sum decomposition suitable for applying the classical linking theorem. We use an abstract linking theorem based on the cohomological index proved in (Yang and Perera, Ann. Sci. Norm. Super. Pisa Cl. Sci. doi: 10.2422/2036-2145.201406_004 , 2016) to overcome this difficulty.
Ending Page	25
Page Count	25
Starting Page	1
File Format	PDF
ISSN	09442669
e-ISSN	14320835
Journal	Calculus of Variations and Partial Differential Equations
Issue Number	4
Volume Number	55
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-07-27
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Variational methods Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Fractional partial differential equations Quasilinear elliptic equations with $p$ -Laplacian Critical exponents
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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