To the uniqueness problem for nonlinear elliptic equations Original Research Article

We prove existence and uniqueness of solutions u∈W1,2(Ω)∩L∞(Ω) to equations of the form View the MathML source Our nonstandard assumptions on the coefficients are such that View the MathML source is concave and a(x,u,ξ)/ρ(u) is increasing in u. Such assumptions are natural in view of drift diffusion processes for example in semiconductors and chemotaxis.