Best constants for Sobolev inequalities for higher order fractional derivatives

By A. Cotsiolis, N. Tavoularis. 2004

394 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/23850fe324bad2c7e6fba0e9e78d2b01c452b7ae

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On critical systems involving fractional Laplacian (2017, neutral): “Then, by [3], Ss is attained by ũ(x) = κ ( ε2 + |x − x0| )−N−2s 2 , i.”
Multiplicity and concentration of positive solutions for the fractional Schrödinger–Poisson systems with critical growth (2017, neutral): “For any α ∈ (0 , 1) , Lemma 2.2 (see [14]) .”
Fractional Gagliardo–Nirenberg and Hardy inequalities under Lorentz norms (2012, background): “Cotsiolis and Tavoularis in [14,15] have studied (1.”
A critical fractional equation with concave-convex power nonlinearities (2013, background): “By [26] (see also [13, 38]) the infimum in (1.”
On fractional Schr\"odinger equations in (\mathbb{R}^N) without the Ambrosetti-Rabinowitz condition (2012, background): “See [8] for a discussion about Sand its minimizers.”
Some constructions for the fractional Laplacian on noncompact manifolds (2012, background): “After all this discussion, one may show, as in the real case ([11], [18]), that: Theorem 2.”
Fractional elliptic problems with critical growth in the whole of $\R^n$ (2015, neutral): “The explicit form of the fractional Sobolev minimizers was found in [23] and it is given by (2.”
Fractional conformal Laplacians and fractional Yamabe problems (2010, background): “In our case, the relevant sharp weighted trace Sobolev inequality appeared in the works [31], [12], [37]: Proposition 1.”
On Fractional Laplacians (2013, background): “In [7] it has been shown that the best constant”