We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem.
Biagi, S., Dipierro, S., Valdinoci, E., Vecchi, E. (2025). A Brezis-Nirenberg type result for mixed local and nonlocal operators. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 32(4), 1-28 [10.1007/s00030-025-01068-0].
A Brezis-Nirenberg type result for mixed local and nonlocal operators
Biagi, Stefano
;Dipierro, Serena;Valdinoci, Enrico;Vecchi, Eugenio
2025
Abstract
We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem.File in questo prodotto:
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