论文标题
列源保留全线非局部抛物线方程的属性
Quasiconvexity preserving property for fully nonlinear nonlocal parabolic equations
论文作者
论文摘要
本文涉及一类具有单调非本地术语的完全非线性抛物线方程。我们研究了阳性，空间胁迫粘度溶液的准分性保留性能。我们证明，如果初始值是Quasiconvex，则库奇问题的粘度解决方案一直在空间中一直存在。由于指数倾向于无穷大，我们的证明可以被视为功率凸的限制版本。我们还提供了几个具体示例，以显示我们结果的应用。
This paper is concerned with a general class of fully nonlinear parabolic equations with monotone nonlocal terms. We investigate the quasiconvexity preserving property of positive, spatially coercive viscosity solutions. We prove that if the initial value is quasiconvex, the viscosity solution to the Cauchy problem stays quasiconvex in space for all time. Our proof can be regarded as a limit version of that for power convexity preservation as the exponent tends to infinity. We also present several concrete examples to show applications of our result.
