A Brezis-Oswald approach for mixed local and nonlocal operators

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., $\mathcal{L}_{p,s} = -Δ_p + (-Δ)^s_p.$ Our main result is resemblant to the celebrated work by Brezis-Oswald [10]. In addition, we prove a regularity result of independent interest.

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