Quasiconvexity preserving property for fully nonlinear nonlocal parabolic equations

被引：0
作者：
Takashi Kagaya
Qing Liu
Hiroyoshi Mitake
机构：
[1] Muroran Institute of Technology,Graduate school of Engineering
[2] Okinawa Institute of Science and Technology Graduate University,Geometric Partial Differential Equations Unit
[3] University of Tokyo,Graduate School of Mathematical Sciences
来源：
Nonlinear Differential Equations and Applications NoDEA | 2023年 / 30卷
关键词：
Quasiconvexity; Nonlocal parabolic equations; Viscosity solutions; Comparison principle; 35D40; 35K15; 52A01;
D O I：
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学科分类号：
摘要：
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.
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