A Brezis-Nirenberg result for non-local critical equations in low dimension

By Raffaella Servadei, Enrico Valdinoci. 2013

234 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5e0bd6f21785fcad19bbef7a9a36152a2cdb4525

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

The Nehari manifold for fractional systems involving critical nonlinearities (2015, unknown): “We refer to [12,23,25,28,29,31,34] for the subcritical case and to [3,4,11,14,15,22,24,26,30] for the critical case.”
The Brezis–Nirenberg problem for the fractional p-Laplacian (2015, background): “2 [44] R. Servadei, E. Valdinoci.”
WEAK AND VISCOSITY SOLUTIONS OF THE FRACTIONAL LAPLACE EQUATION (2014, unknown): “, [12, 14] and references therein).”
Multiplicity and concentration of positive solutions for the fractional Schrödinger–Poisson systems with critical growth (2017, unknown): “See for example [12, 13, 22, 23, 28, 37].”
Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity (2014, background): “ space, the choice of this functional space is an improvement with respect of the usual space X0 = {u ∈ X : u = 0 a.e. in Rn \ Ω}, where many authors set their nonlocal variational problems, e.g. [5]–[12, 22, 27]–[29]. Indeed, the density result proved in [19, Theorem 6] does not hold true without m”
Bifurcation and multiplicity results for critical fractional p‐Laplacian problems (2014, unknown): “, [34, 31, 35, 32, 33, 2, 5, 37, 17]).”
DENSITY PROPERTIES FOR FRACTIONAL SOBOLEV SPACES (2015, background): “Recently, in the literature a deep interest was shown for nonlocal operators, thanks to their intriguing analytical structure and in view of several applications in a wide range of contexts, such as the thin obstacle problem, optimization, finance, phase transitions, stratified materials, anomalous ”
A bifurcation result for non-local fractional equations (2015, background): “In [4] [7] [8] [11] [19] [20] [21] [23] [24] [25] [26] [27] [30] (see also the references therein) the authors studied non-local fractional Laplacian equations with superlinear and subcritical or critical nonlinearities, while in [12] [13] the asymptotically linear case was exploited.”
Nonlocal problems with critical Hardy nonlinearity (2017, result): “– Comparison with some previous results The fractional Brezis-Nirenberg case r = p, α = 0, q = p∗ has been considered in [24, 25] when p = 2 and in [19] for any p > 1; the paper [33] deals with the quasilinear Brezis-Nirenberg problem with Hardy-Sobolev nonlinearity, i.”
A critical Kirchhoff type problem involving a nonlocal operator (2013, background): “Recently, some studies have been performed for critical problems in a non-local setting; we refer the interested readers to [3, 6, 17, 18, 19, 20].”