论文标题
椭圆形和抛物线双相方程的渐近平均值特性
Asymptotic mean value properties for the elliptic and parabolic double phase equations
论文作者
论文摘要
我们在粘度意义上表征了双相椭圆方程$$ - {\ rm div}（\ lvert \ nabla u \ rvert^{p-2} \ nabla u+ a（x） u_t = \ lvert \ nabla u \ rvert^{2-p} {\ rm div}（\ lvert \ nabla u \ rvert^{p-2} \ nabla u+ a（x，x，x，x，x，t） $$这是这种不均匀椭圆形和抛物线方程的第一个平均值结果。此外，获得的结果也可以应用于$ p（x）$ - 拉普拉斯方程和可变系数$ p $ -laplace类型方程。
We characterize an asymptotic mean value formula in the viscosity sense for the double phase elliptic equation $$ -{\rm div}(\lvert \nabla u \rvert^{p-2}\nabla u+ a(x)\lvert\nabla u \rvert^{q-2}\nabla u)=0 $$ and the normalized double phase parabolic equation $$ u_t=\lvert\nabla u \rvert ^{2-p}{\rm div}(\lvert \nabla u \rvert^{p-2}\nabla u+ a(x,t)\lvert\nabla u \rvert^{q-2}\nabla u), \quad 1<p\leq q<\infty. $$ This is the first mean value result for such kind of nonuniformly elliptic and parabolic equations. In addition, the results obtained can also be applied to the $p(x)$-Laplace equations and the variable coefficient $p$-Laplace type equations.
