Work

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

Year: 2026

Type: article

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 , 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.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70477

Authors: Stefano Biagi, Serena Dipierro, Enrico Valdinoci, Eugenio Vecchi

Institutions: Politecnico di Milano, The University of Western Australia, University of Bologna

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Australian Mathematical Society, Australian Research Council