We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. The main novelty is that we consider a mixed operator of the form (Formula presented.), namely we suppose that the fractional Laplacian has the “wrong sign” and can be seen as a nonlocal perturbation of the purely local case, which is needed to produce a nontrivial solution of the critical problem.
Biagi, S., Dipierro, S., Valdinoci, E., Vecchi, E. (2026). On a Sobolev critical problem for the superposition of a local and nonlocal operator with the “wrong sign”. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 58(9), 1-18 [10.1112/blms.70477].
On a Sobolev critical problem for the superposition of a local and nonlocal operator with the “wrong sign”
Dipierro S.;Valdinoci E.;Vecchi E.
2026
Abstract
We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. The main novelty is that we consider a mixed operator of the form (Formula presented.), namely we suppose that the fractional Laplacian has the “wrong sign” and can be seen as a nonlocal perturbation of the purely local case, which is needed to produce a nontrivial solution of the critical problem.| File | Dimensione | Formato | |
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