时间依赖的Hessian商不等式正解的不存在性

Nonexistence of positive solutions to time-dependent Hessian quotient inequalities

考虑两类相关的时间依赖的Hessian商不等式,第一类不等式与平均场博弈论有关,第二类不等式属于抛物型完全非线性不等式.针对这两类不等式,假设全局正的容许解存在,构造两个合适的测试函数,借助Schwarz和Young不等式计算推出矛盾,从而证明了它们的全局正容许解的不存在性.该结果可视作判定这两类不等式全局正容许解不存在性的充分条件.

This paper considered two types of time-dependent Hessian quotient inequalities.The first kind of inequality was related to the mean field games theory and the second category of inequality belonged to parabolic fully nonlinear inequality.In order to prove the nonexistence of their entire positive admissible solutions,the existence of entire positive admissible solutions was assumed on the contrary,and two suitable test functions were constructed.With the help of Schwarz’s inequality and Young’s inequality,the contradiction was derived by delicate calculations.The result of this paper could be regarded as sufficient conditions to determine the nonexistence of entire positive admissible solutions to these two inequalities.