Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms
Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms
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DOI：
10.1016/j.jmaa.2011.03.009
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发表时间：
2010-10
期刊：
影响因子：
--
通讯作者：
Shigeaki Koike;Olivier Ley
中科院分区：
文献类型：
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作者：
Shigeaki Koike;Olivier Ley
研究了关于Du的具有超线性项的完全非线性可能退化椭圆型偏微分方程，证明了在某些多项式型增长条件下可能无界的粘性解之间的几个比较原理.我们的主要结果适用于具有凸超线性项的偏微分方程，但我们也得到了一些非凸情况下的结果。应用单调系统的偏微分方程。
We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to Du. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.