相关论文: Gradient estimates for a nonlinear parabolic equat…

This article presents new local and global gradient estimates of Li-Yau type for positive solutions to a class of nonlinear elliptic equations on smooth metric measure spaces involving the Witten Laplacian. The estimates are derived under…

In this paper we prove gradient estimates of both elliptic and parabolic types, specifically, of Souplet-Zhang, Hamilton and Li-Yau types for positive smooth solutions to a class of nonlinear parabolic equations involving the Witten or…

In this article we present new gradient estimates for positive solutions to a class of nonlinear elliptic equations involving the f-Laplacian on a smooth metric measure space. The gradient estimates of interest are of Souplet-Zhang and…

This article presents new gradient estimates for positive solutions to the nonlinear fast diffusion equation on smooth metric measure spaces, involving the $f$-Laplacian. The gradient estimates of interest are mainly of…

We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space. As applications, we determine various conditions on the equation's coefficients…

In this paper we prove some Hamilton type and Li-Yau type gradient estimates on positive solutions to generalized nonlinear parabolic equations on smooth metric measure space with compact boundary. The geometry of the space in terms of…

In this paper, we prove Souplet-Zhang type gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with the compact boundary under the Dirichlet boundary condition when the Bakry-Emery Ricci tensor and the…

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…

Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with $\infty$-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation…

We consider gradient estimates to positive solutions of porous medium equations and fast diffusion equations: $$u_t=\Delta_\phi(u^p)$$ associated with the Witten Laplacian on Riemannian manifolds. Under the assumption that the…

In this paper, we consider the nonlinear elliptic equation $$\Delta_fv^\tau+\lambda v=0$$ on a complete smooth metric measure space with $m$-Bakry-\'{E}mery Ricci curvature bounded from below, where $\tau>0$ and $\lambda$ are constant. We…

This article presents new gradient estimates for positive solutions to the nonlinear porous medium equation (NPME) in the context of smooth metric measure spaces. The diffusion operator here is the f-Laplacian and the gradient estimates of…

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)=\Delta u(x,t)+a u(x,t)(\log u(x,t))^b +…

This article is devoted to the study of several estimations for a positive solution to a nonlinear weighted parabolic equation on a weighted Riemannian manifold. We therefore derive new Li-Yau type and Hamilton type gradient estimates…

We derive logarithmic gradient estimate and universal boundedness estimate for semilinear elliptic equations on \RCD\, metric measure spaces, which contains the class of Riemannian manifolds with Ricci curvature bounded below. These…

This paper is the first in a series of paper where we describe the differential operators on general nonlinear metric measure spaces, namely, the Finsler spaces. We try to propose a general method for gradient estimates of the positive…

Let $(N, g)$ be a complete noncompact Riemannian manifold with Ricci curvature bounded from below. In this paper, we study the gradient estimates of positive solutions to a class of nonlinear elliptic equations $$\Delta u(x)+a(x)u(x)\log…

Let $(M,g(t))$, $0\le t\le T$, be a n-dimensional complete noncompact manifold, $n\ge 2$, with bounded curvatures and metric $g(t)$ evolving by the Ricci flow $\frac{\partial g_{ij}}{\partial t}=-2R_{ij}$. We will extend the result of L. Ma…

On a Riemannian metric-measure space, we establish an Alexandrov-Bakelman-Pucci type measure estimate connecting Bakry-\'Emery Ricci curvature lower bound, modified Laplacian and the measure of certain special sets. We apply this estimate…

Let $(M, g)$ be an dimensional complete Riemannian manifold. In this paper we prove local Li-Yau type gradient estimates for all positive solutions to the following nonlinear parabolic equation \begin{equation*} (\partial_t - \Delta_g +…