Abstract
In this paper, we obtain the existence of a nontrivial solution for a class of singular quasilinear elliptic equations in weighted Sobolev spaces. The proofs rely on Galerkin-type techniques, Brouwer fixed point theorem, and a new weighted compact Sobolev-type embedding theorem established by Shapiro. The equation is one of the most useful sets of Navier-Stokes equations, which describe the motion of viscous fluid substances such as liquids, gases and so on.
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Foundation item: the National Natural Science Foundation of China (10471063) and by Innovation Programm of Shanghai Municipal Education Commission (08YZ94).
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Jia, G., Zhao, Q. Existence Results in Weighted Sobolev Spaces for Some Singular Quasilinear Elliptic Equations. Acta Appl Math 109, 599–607 (2010). https://doi.org/10.1007/s10440-008-9336-x
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DOI: https://doi.org/10.1007/s10440-008-9336-x