We establish regularity results for weak solutions of Robin problems driven by the well-known Orlicz g-Laplacian operator given by P \(\begin{aligned} \left\{ \begin{array}{ll} -\Delta _g u=f(x,u),& x\in \Omega \\ \displaystyle a(\vert \nabla u\vert )\frac{\partial u}{d\nu }+b(x)\vert u\vert ^{p-2}u=0,& x\in \partial \Omega , \end{array} \right. \end{aligned}\) where \(\Delta _g u:=\text {div}(a(\vert \nabla u\vert )\nabla u)\) , \(\Omega \subset \mathbb {R}^N,\ N\ge 3\) , is a bounded domain with \(C^2\) -boundary \(\partial \Omega \) , \(\frac{\partial u}{d\nu }=\nabla u \cdot \nu \) , \(\nu \) is the unit exterior vector on \(\partial \Omega \) , \(p>0\) , \(b \in C^{1,\theta }(\partial \Omega )\) with \(\theta \in (0,1)\) and \(\inf _{x\in \partial \Omega } b(x) > 0\) . Specifically, using a suitable variation of the Moser iteration technique, we prove that every weak solution of the problem (P) is bounded. Moreover, we combine this result with the Lieberman regularity theorem, to show that every \(C^1(\overline{\Omega })\) -local minimizer is also a \(W^{1,G}(\Omega )\) -local minimizer for the corresponding energy functional of problem (P).
