Borderline Variational Problems Involving Fractional Laplacians and Critical Singularities

By Nassif Ghoussoub, Shaya Shakerian. 2015

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Abstract We consider the problem of attainability of the best constant C > 0 in the following critical fractional Hardy-Sobolev inequality: For all , , where and γ ∈ ℝ. This allows us to establish the existence of nontrivial weak solutions for the following doubly critical problem on ℝn, , where is the critical α-fractional Sobolev exponent, and , the latter being the best fractional Hardy constant on ℝn.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d45f1ef4a3b1b88ff54e2f51c9813fe4f698751b