Stationary states of a chemotaxis consumption system with singular sensitivity and inhomogeneous boundary conditions

For given total mass m>0 we show unique solvability of the stationary chemotaxis-consumption model \ cases 0= u - (uv v) \\ 0= v - uv \\ _ u = m cases \ under no-flux-Dirichlet boundary conditions in bounded smooth domains R² and =BR (0) Rᵈ, d 3.