International Journal of Differential Equations
Volume 2011 (2011), Article ID 356356, 17 pages
http://dx.doi.org/10.1155/2011/356356
Research Article

𝐿 ∞ -Solutions for Some Nonlinear Degenerate Elliptic Equations

Albo Carlos Cavalheiro

Department of Mathematics, State University of Londrina, 86051-990 Londrina, PR, Brazil

Received 17 May 2011; Revised 6 October 2011; Accepted 6 October 2011

Academic Editor: Toka Diagana

Copyright © 2011 Albo Carlos Cavalheiro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations − ∑ 𝑛 𝑗 = 1 𝐷 𝑗 [ 𝜔 2 ( 𝑥 ) 𝒜 𝑗 ( 𝑥 , 𝑢 , ∇ 𝑢 ) ] + 𝜔 1 ( 𝑥 ) 𝑔 ( 𝑥 , 𝑢 ( 𝑥 ) ) + 𝐻 ( 𝑥 , 𝑢 , ∇ 𝑢 ) 𝜔 2 ( 𝑥 ) = 𝑓 ( 𝑥 ) , o n Ω in the setting of the weighted Sobolev spaces W 0 1 , 𝑝 ( Ω , 𝜔 1 , 𝜔 2 ) .