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The Dirichlet Problem of Nonhomogeneous Degenerate Nonlinear Elliptic Equations

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发表日期：

2025年11月15日

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Albo Carlos Cavalheiro

摘要

In this paper we are interested in the existence and uniqueness of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations

$\left\{{\matrix{{- {\text{div}}[{\cal{A}}(x,\nabla u)v(x)] + {\cal{B}}(x,u)\omega (x) = {\rho _0} - \sum\limits_{j = 1}^n {{D_j}{\rho _j},}} \hfill \cr {u - \psi \in W_0^{1,p}(\Omega,\omega,v),} \hfill \cr}} \right.$ ${\begin{matrix} - div [A (x, \nabla u) v (x)] + B (x, u) ω (x) = ρ_{0} - \sum_{j = 1}^{n} D_{j} ρ_{j}, \\ u - ψ \in W_{0}^{1, p} (Ω, ω, v), \end{matrix}$ in the setting of the weighted Sobolev spaces.