A transmission problem with (p, q)-Laplacian
Maria Colombo, Sunghan Kim, Henrik Shahgholian · Communications in Partial Differential Equations · 2023
In this paper we consider the so-called double-phase problem where the phase transition takes place across the interface of the positive and negative phase of minimizers of the functional J(v,Ω)=∫Ω(|Dv+|p+|Dv−|q)dx. We prove that minimizers exist, are Hölder regular and verify (q−1)|Du−|q=(p−1)|Du+|p on ∂{u>0}, in a weak sense. We also prove that their free boundary is C1,α a.e. with respect to the measure Δpu+, whose support is of σ-finite (n−1)-dimensional Hausdorff measure.