In this paper, we provide necessary and sufficient conditions for the existence of a unique positive weak solution for some sublinear Dirichlet problems driven by the sum of a quasilinear local and a nonlocal operator, i.e. Lp,s = -Cp + (-C)ps. Our main result is resemblant to the celebrated work by Brezis-Oswald [Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986) 55-64]. In addition, we prove a regularity result of independent interest.

Biagi S., Mugnai D., Vecchi E. (2024). A Brezis-Oswald approach for mixed local and nonlocal operators. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 26(2), 1-28 [10.1142/S0219199722500572].

A Brezis-Oswald approach for mixed local and nonlocal operators

Vecchi E.
2024

Abstract

In this paper, we provide necessary and sufficient conditions for the existence of a unique positive weak solution for some sublinear Dirichlet problems driven by the sum of a quasilinear local and a nonlocal operator, i.e. Lp,s = -Cp + (-C)ps. Our main result is resemblant to the celebrated work by Brezis-Oswald [Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986) 55-64]. In addition, we prove a regularity result of independent interest.
2024
Biagi S., Mugnai D., Vecchi E. (2024). A Brezis-Oswald approach for mixed local and nonlocal operators. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 26(2), 1-28 [10.1142/S0219199722500572].
Biagi S.; Mugnai D.; Vecchi E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/898551
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