Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro

Abstract


In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations \begin{align} {\Delta}(v(x)\, {\vert{\Delta}u\vert}^{p-2}{\Delta}u) &-\sum_{j=1}^n D_j{\bigl[}{\omega}_1(x) \mathcal{A}_j(x, u, {\nabla}u){\bigr]}+ b(x,u,{\nabla}u)\, {\omega}_2(x)\\ & = f_0(x) - \sum_{j=1}^nD_jf_j(x), \ \ {\rm in } \ \ {\Omega} \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.2016.70.2.9
Data publikacji: 2016-12-24 22:42:00
Data złożenia artykułu: 2016-12-22 23:18:14

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