The existence of solutions to the nonhomogeneous degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro

Abstract


In this paper we are interested in the existence and uniqueness  of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations
\begin{align*}&- \mathrm{div}\big[{\mathcal{A}}(x, {\nabla}u)\, {\omega}_2(x)
+ {\mathcal{B}}(x, {\nabla}u)\, {\nu}_1(x)\big] + {\mathcal{H}}(x,u,{\nabla}u){\nu}_2 + {\vert u \vert}^{p-2}u\,{\omega}_1\\
&= {\rho}_0 - \sum_{j=1}^nD_j{\rho}_j,\\ &  u - {\psi}\, {\in}\, W_0^{1,p}(\Omega , {\omega}_1 , {\omega}_2),\end{align*}
in the setting of the weighted Sobolev spaces.


Keywords


Degenerate nonlinear elliptic equations; weighted Sobolev spaces

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References


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DOI: http://dx.doi.org/10.17951/a.2025.79.2.17-37
Date of publication: 2025-12-31 17:49:59
Date of submission: 2025-12-30 20:39:52


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