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.| File | Dimensione | Formato | |
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A brezis-oswald approach for mixed local and nonlocal operators.pdf
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