ﻻ يوجد ملخص باللغة العربية
In this paper we shall establish some Liouville theorems for solutions bounded from below to certain linear elliptic equations on the upper half space. In particular, we show that for $a in (0, 1)$ constants are the only $C^1$ up to the boundary positive solutions to $div(x_n^a abla u)=0$ on the upper half space.
In this paper we shall classify all positive solutions of $ Delta u =a u^p$ on the upper half space $ H =Bbb{R}_+^n$ with nonlinear boundary condition $ {partial u}/{partial t}= - b u^q $ on $partial H$ for both positive parameters $a, b>0$. We will
There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent $lambda=n-alpha$ (that is for the c
We study a class of second-order degenerate linear parabolic equations in divergence form in $(-infty, T) times mathbb R^d_+$ with homogeneous Dirichlet boundary condition on $(-infty, T) times partial mathbb R^d_+$, where $mathbb R^d_+ = {x in mathb
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on fini
In this paper we establish the reversed sharp Hardy-Littlewood-Sobolev (HLS for short) inequality on the upper half space and obtain a new HLS type integral inequality on the upper half space (extending an inequality found by Hang, Wang and Yan in ci