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arXiv · 2601.07521

On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign''

Stefano Biagi·Serena Dipierro·Enrico Valdinoci·Eugenio Vecchi
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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 $-Δ- γ(-Δ)^s$, 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.

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Stefano Biagi, Serena Dipierro, Enrico Valdinoci, Eugenio Vecchi. 2026-07-27. On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign''. https://arxiv.org/abs/2601.07521

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