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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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Official URL: http://journals.cambridge.org/abstract_S0308210500013822

## Abstract

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 |
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Uncontrolled Keywords: | Nonlinear elliptic equations |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15615 |

Deposited On: | 13 Jun 2012 09:23 |

Last Modified: | 12 Dec 2018 15:08 |

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