Entropy solutions for nonlinear elliptic anisotropic problem with Robin boundary condition (Q2868754)

Let \(\Omega\) be an open bounded domain of \(\mathbb{R}^N\) (\(N\geq 3\)) with a smooth boundary. This paper is mainly concerned with the existence and uniqueness of an entropy solution to the following nonlinear anisotropic elliptic problem: NEWLINE\[NEWLINE-\sum_{i=1}^N \frac{\partial }{\partial x_i}a_i(x,\frac{\partial }{\partial x_i} u)+|u|^{p_M(x)-2}u=f\;in\;\OmegaNEWLINE\]NEWLINE with boundary condition NEWLINE\[NEWLINE\sum_{i=1}^N a_i(x,\frac{\partial }{\partial x_i} u)\nu_i=-|u|^{r(x)-2}u\;on\;\partial\Omega,NEWLINE\]NEWLINE where \(f\in L^1(\Omega)\) and \(\nu_i(x)\) are the outer unit normals to the boundary at \(x\in \partial\Omega\).