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The Brezis-Nirenberg problem for the fractional \(p\)-Laplacian. (English) Zbl 1361.35198
This paper is concerned with the study of the Brezis-Nirenberg problem in the abstract setting corresponding to fractional \(p\)-Laplace operators. The main result of this paper establishes the existence of nontrivial weak solutions in several contexts. The proof combines several arguments including the study of the associated minimization problem, regularity estimates and a related linking theorem based on the cohomological index.

MSC:
35R11 Fractional partial differential equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35B33 Critical exponents in context of PDEs
35A15 Variational methods applied to PDEs
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