Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations
Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations
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DOI：
10.1007/s000130050221
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发表时间：
1998-06
影响因子：
0.6
通讯作者：
B. Kawohl;N. Kutev
中科院分区：
文献类型：
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作者：
B. Kawohl;N. Kutev
给出了完全非线性椭圆型方程上半连续粘性子解的强极大值原理，它对空间变量的依赖可能是不连续的。我们的结果改进了前人关于线性[18]和非线性[22]方程的相关结果，因为我们削弱了关于非线性的结构性假设。反例表明，我们的结果是最优的。此外，它们还得到了比较和唯一性结果的补充，其中粘性下解与分段经典上解进行了比较。奇怪的是，完全非线性问题的分段经典解的存在意味着它在更大类连续粘性解中的唯一性。
We derive a strong maximum principle for upper semicontinuous viscosity subsolutions of fully nonlinear elliptic differential equations whose dependence on the spatial variables may be discontinuous. Our results improve previous related ones for linear [18] and nonlinear [22] equations because we weaken structural assumptions on the nonlinearities. Counterexamples show that our results are optimal. Moreover they are complemented by comparison and uniqueness results, in which a viscosity subsolution is compared with a piecewise classical supersolution. It is curious to note that existence of a piecewise classical solution to a fully nonlinear problem implies its uniqueness in the larger class of continuous viscosity solutions.