ﻻ يوجد ملخص باللغة العربية
We derive a matrix version of Li & Yau--type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parallel Ricci tensor, similarly to what R.~Hamilton did in~cite{hamilton7} for the standard heat equation. We then apply these estimates to obtain some Harnack--type inequalities, which give local bounds on the solutions in terms of the geometric quantities involved.
We give some a priori estimates of type sup*inf for Yamabe and prescribed scalar curvature type equations on Riemannian manifolds of dimension >2. The product sup*inf is caracteristic of those equations, like the usual Harnack inequalities for non ne
We show a triviality result for pointwise monotone in time, bounded eternal solutions of the semilinear heat equation begin{equation*} u_{t}=Delta u + |u|^{p} end{equation*} on complete Riemannian manifolds of dimension $n geq 5$ with nonnegative Ric
We give a direct analytic proof of the classical Boundary Harnack inequality for solutions to linear uniformly elliptic equations in either divergence or non-divergence form.
We consider second-order linear parabolic operators in non-divergence form that are intrinsically defined on Riemannian manifolds. In the elliptic case, Cabre proved a global Krylov-Safonov Harnack inequality under the assumption that the sectional c
We consider nonnegative solutions $u:Omegalongrightarrow mathbb{R}$ of second order hypoelliptic equations begin{equation*} mathscr{L} u(x) =sum_{i,j=1}^n partial_{x_i} left(a_{ij}(x)partial_{x_j} u(x) right) + sum_{i=1}^n b_i(x) partial_{x_i} u(x) =