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Keywords:
degenerate nolinear elliptic equations; weighted Sobolev spaces; Navier problem
degenerate nolinear elliptic equations; weighted Sobolev spaces; Navier problem
Summary:
In this paper we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations \begin {equation*} \Delta (v(x)\,\vert \Delta u\vert ^{q-2}\Delta u) -\sum _{j=1}^n D_j\bigl [\omega (x) {\cal A}_j(x, u, {\nabla }u)\bigr ] = f_0(x) - \sum _{j=1}^nD_jf_j(x), \text { in }\Omega \end {equation*} in the setting of the weighted Sobolev spaces.
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