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On some nonlinear elliptic-equations involving derivatives of the nonlinearity


Carrillo Menéndez, José and Chipot, Michel (1985) On some nonlinear elliptic-equations involving derivatives of the nonlinearity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 100 (Part 3). pp. 281-294. ISSN 0308-2105

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The existence of weak solutions of the Dirichlet problem for nonlinear elliptic equations of the type −(∂/∂x j )(a ij (x)u x i +b j (u))+a(x)u=f is proved for nonlinearities b j which are only continuous. The proof is based on the observation that an L ∞ a priori estimate is valid which is independent of b j . The second part contains several uniqueness results and counterexamples, showing that uniqueness may fail in general.

Item Type:Article
Uncontrolled Keywords:Nonlinear elliptic equations
Subjects:Sciences > Mathematics > Differential equations
ID Code:15615

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Deposited On:13 Jun 2012 09:23
Last Modified:06 Feb 2014 10:28

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