Consider following problem for Poisson equation in some bounded domain $G$ with piecewise smooth Lipschitz continuious boundary $\partial G$: $$ -\Delta u = \rho \text{ in } G\\ (\boldsymbol{\nu} \nabla) u = \sigma \text{ on } \partial G $$ where vector $\boldsymbol{\nu}$ is neither collinear to the normal $\mathbf{n}$ nor orthogonal to it.
Assuming all required smoothness, is the problem posessed well?