The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order

Abstract

In this paper, we study the existence of minimizers of the Sobolev quotient for a class of nonlocal operators with an orthotropic structure having different exponents of integrability and different orders of differentiability. Our method is based on the concentration-compactness principle which we extend to this class of operators. One consequence of our main result is the existence of a nontrivial nonnegative solution to the corresponding critical problem.

arXiv comment19 pages

References in corpus (5)

• The concentration-compactness principle for variable exponent spaces and applications
• Extremal functions for the anisotropic Sobolev inequalities
• Multiplicity results for $(p,q)$ fractional elliptic equations involving critical nonlinearities
• Regularity estimates for fractional orthotropic $p$-Laplacians of mixed order
• Anisotropic p-Laplacian Evolution of Fast Diffusion type

Cited by in corpus (1)

• On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications