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Existence results for a class of nonlinear elliptic problems with p-growth in the gradient

✍ Scribed by Nathalie Grenon; Cristina Trombetti

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
123 KB
Volume
52
Category
Article
ISSN
0362-546X

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✦ Synopsis

We prove the existence of bounded solutions for a class of nonlinear elliptic problems whose model is in the form: -div(a(x; u; Du)) = k1(|u|)|Du| p + k2(|u|)f; u ∈ W 1;p 0 ( ) ∩ L ∞ ( ); (*) where a(x; Á; ) ¿ b(|Á|)| | p , b is a continuous monotone decreasing function and k1 and k2 are continuous monotone increasing functions.

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✍ Basilio Messano πŸ“‚ Article πŸ“… 2006 πŸ› Elsevier Science 🌐 English βš– 185 KB

In this paper we study the Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = H (x, u, Du)+g (x, u), where the principal term is a Leray-Lions operator defined on W 1,p 0 ( ). Comparison results are obtained between the rearrangement of a solution u of Dirichlet problem