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

Fuente: arXiv
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Autori principali: Biagi, Stefano, Dipierro, Serena, Valdinoci, Enrico, Vecchi, Eugenio
Natura: Preprint
Pubblicazione: 2026
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author Biagi, Stefano
Dipierro, Serena
Valdinoci, Enrico
Vecchi, Eugenio
author_facet Biagi, Stefano
Dipierro, Serena
Valdinoci, Enrico
Vecchi, Eugenio
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_07521
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign''
Biagi, Stefano
Dipierro, Serena
Valdinoci, Enrico
Vecchi, Eugenio
Analysis of PDEs
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.
title On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign''
topic Analysis of PDEs
url https://arxiv.org/abs/2601.07521