Existence and uniqueness results for parabolic equations with Robin type boundary conditions in a non-regular domain of R3

This paper is devoted to the analysis of the following two-space dimensional linear parabolic equation ∂tu-∂x12u-∂x22u=f, subject to Robin type conditions ∂x1u+βu=0, on the lateral boundary, where the coefficient β satisfies suitable non-degeneracy assumptions. The right-hand side f of the equation is taken in L2. The problem is set in a domain of the form t,x1∈R2:0