Quasiconcave Solutions to Elliptic Problems in Convex Rings
Quasiconcave Solutions to Elliptic Problems in Convex Rings
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DOI：
10.1512/iumj.2009.58.3539
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发表时间：
2009
影响因子：
1.1
通讯作者：
C. Bianchini;M. Longinetti;P. Salani
中科院分区：
文献类型：
--
作者：
C. Bianchini;M. Longinetti;P. Salani
研究了凸环Ω中一般椭圆型方程解的水平集的凸性。特别地，如果u是一个经典解，它在Ω的两个连通分量上具有常数（不同）值，我们考虑它的拟凹包络u*（即，的功能，其上级集是凸包络的那些u），我们找到适当的假设，迫使u * 是一个子解的方程。如果比较原理成立，则得到u = u*，然后u是拟凹的。
We investigate the convexity of level sets of solutions to general elliptic equations in a convex ring Ω. In particular, if u is a classical solution which has constant (distinct) values on the two connected components of ∂Ω, we consider its quasi-concave envelope u* (i.e., the function whose superlevel sets are the convex envelopes of those of u) and we find suitable assumptions which force u * to be a subsolution of the equation. If a comparison principle holds, this yields u = u* and then u is quasi-concave.