Study of Certain Navier Problems in Sobolev Space with Weights

Abstract

In this paper, we study the following Navier problem

Here, $h ∈ L^{p'} (\mathcal{Q}, v^{1−p′}_1),$ $\mathcal{K}, \mathcal{L}$ and $b$ are Carathéodory functions and $ϕ_1,ϕ_2,$ $v_1, v_2, v_3$ and $v_4$ are $A_p$-weights functions. By using the theory of monotone operators (Browder–Minty Theorem), we demonstrate the existence and uniqueness of weak solution to the above problem.