Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:420

Article

Arcoya, David¹  De Coster, Colette²  Jeanjean, Louis³  Tanaka, Kazunaga⁴ 

[1] Univ Granada, Dept Math Anal, E-18071 Granada, Spain

[2] Univ Valenciennes & Hainaut Cambresis, Inst Sci & Techn Valenciennes, LAMAV, FR CNRS 2956, F-59313 Valenciennes 9, France

[3] Univ Franche Comte, Math Lab, UMR 6623, F-25030 Besancon, France

[4] Waseda Univ, Sch Sci & Engn, Dept Math, Shijuku Ku, Tokyo, Tokyo 1698555, Japan

关键词: Quasilinear elliptic equations;    Quadratic growth in the gradient;    Uniqueness of solution;   

DOI  :  10.1016/j.jmaa.2014.06.007

来源: Elsevier

【 摘 要 】

In this note we present some uniqueness and comparison results for a class of problem of the form -Lu = H(x, u, del u) + h(x), u is an element of H-0(1)(Omega) boolean AND L-infinity(Omega), (0.1) where Omega subset of R-N, N >= 2 is a bounded domain, L is a general elliptic second order linear operator with bounded coefficients and H is allowed to have a critical growth in the gradient. In some cases our assumptions prove to be sharp. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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