Geodesic
Existence and uniqueness of solutions for some degenerate nonlinear elliptic equations
Archivum mathematicum, Tome 50 (2014) no. 1, pp. 51-63 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with 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 }(x) {\mathcal{A}}_j(x, u, {\nabla }u){\bigr ]}\\ =\ f_0(x) - \sum _{j=1}^nD_jf_j(x)\,, \quad \mbox {in}\quad {\Omega }\end{align*} in the setting of the weighted Sobolev spaces.
In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with 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 }(x) {\mathcal{A}}_j(x, u, {\nabla }u){\bigr ]}\\ =\ f_0(x) - \sum _{j=1}^nD_jf_j(x)\,, \quad \mbox {in}\quad {\Omega }\end{align*} in the setting of the weighted Sobolev spaces.
DOI : 10.5817/AM2014-1-51
Classification : 35J60, 35J70
Keywords: degenerate nolinear elliptic equations; weighted Sobolev spaces 
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Cavalheiro, Albo Carlos. Existence and uniqueness of solutions for some degenerate nonlinear elliptic equations. Archivum mathematicum, Tome 50 (2014) no. 1, pp. 51-63. doi: 10.5817/AM2014-1-51

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