Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms

Authors:	Nathalie Grenon François Murat Alessio Porretta

Institution:	1. Centre universitaire de Bourges, rue Gaston Berger, BP 4043, 18028 Bourges cedex, France;2. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75252 Paris cedex 05, France;3. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy

Abstract:	In this Note we prove an a priori estimate and the existence of a solution for a class of nonlinear elliptic problems whose model is $? div A (x) D u + α_{0} u = γ {\| D u \|}^{q} + f (x)$ , when $1 < q < 2$ and $f \in L^{m} (Ω)$ for some suitable m. The main interest of the result lies in the a priori estimate, the complete proof of which is given in the Note. *To cite this article: N. Grenon et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).*

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