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convection term

Proceedings of the Edinburgh Mathematical Society (1)

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Comparison and Positive Solutions for Problems with the (p, q)-Laplacian and a Convection Term
Luiz F. O. Faria, Olímpio H. Miyagaki, Dumitru Motreanu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 3 / October 2014

Published online by Cambridge University Press:

16 April 2014, pp. 687-698
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The aim of this paper is to prove the existence of a positive solution for a quasi-linear elliptic problem involving the (p, q)-Laplacian and a convection term, which means an expression that is not in the principal part and depends on the solution and its gradient. The solution is constructed through an approximating process based on gradient bounds and regularity up to the boundary. The positivity of the solution is shown by applying a new comparison principle, which is established here.