CONTINUITY OF SOLUTIONS OF A NONLINEAR ELLIPTIC EQUATION

被引：0
|
作者：
Bousquet, Pierre [1 ]
机构：
[1] Univ Aix Marseille 1, LATP, UMR6632, F-13331 Marseille 3, France
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2013年 / 19卷 / 01期
关键词：
Nonlinear elliptic equations; continuity of solutions; lower bounded slope condition; Lavrentiev phenomenon; DIFFERENTIAL-FUNCTIONAL EQUATIONS;
D O I：
10.1051/cocv/2011194
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We consider a nonlinear elliptic equation of the form div [a(del u)] + F[u] = 0 on a domain Omega, subject to a Dirichlet boundary condition tr u = phi. We do not assume that the higher order term a satisfies growth conditions from above. We prove the existence of continuous solutions either when Omega is convex and phi satisfies a one-sided bounded slope condition, or when a is radial: a(xi) = l(vertical bar xi vertical bar)/vertical bar xi vertical bar xi for some increasing l : R+ -> R+.
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页码：1 / 19
页数：19
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