Harnack inequality for quasilinear elliptic equations in generalized Orlicz-Sobolev spaces
The authors prove the Harnack inequality for positive solutions of quasilinear elliptic equations in the generalized Orlicz-Sobolev space setting. Their approach is based on the usage of the upper envelope function \(G^+\) of a \(\Phi\)-function \(G(\cdot)\) and the Moser's iteration technique. Assuming a structure condition on \(G(\cdot)\) and a Harnack condition introduced by \textit{P. Harjulehto} et al. [Calc. Var. Partial Differ. Equ. 56, No. 2, Paper No. 22, 26 p. (2017; Zbl 1366.35036)], they get the Hölder continuity of bounded solutions. We recall that such regularity result was proved in previuos papers but using completely different approaches.
scientific article; zbMATH DE number 7223214