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arXiv · 2105.13612

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

Jamil Chaker·Minhyun Kim·Marvin Weidner
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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.

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Jamil Chaker, Minhyun Kim, Marvin Weidner. 2021-05-28. The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order. https://doi.org/10.1016/j.na.2023.113254

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