论文标题
在整体RICCI曲率边界下非线性抛物线方程的HARNACK不平等
Harnack inequality for nonlinear parabolic equations under integral Ricci curvature bounds
论文作者
论文摘要
令$（m^{n}，g）$为完整的Riemannian歧管。 In this paper, we establish a space-time gradient estimates for positive solutions of nonlinear parabolic equations $$\partial_{t}u(x,t)=Δu(x,t)+a u(x,t)(\log u(x,t))^b + q(x,t)A(u(x,t)),$$ on geodesic balls $B(O,r)$ in $M$ with $ 0 <r \ leq r $ for $ p> \ frac {n} {2} $当积分ricci曲率$ k（p，1）$很小时。通过整合梯度估计，我们发现相应的Harnack不平等现象。
Let $(M^{n},g)$ be a complete Riemannian manifold. In this paper, we establish a space-time gradient estimates for positive solutions of nonlinear parabolic equations $$\partial_{t}u(x,t)=Δu(x,t)+a u(x,t)(\log u(x,t))^b + q(x,t)A(u(x,t)),$$ on geodesic balls $B(O,r)$ in $M$ with $0<r\leq r$ for $p>\frac{n}{2}$ when integral Ricci curvature $k(p,1)$ is small enough. By integrating the gradient estimates, we find the corresponding Harnack inequalities.
