harnack type inequality
Recently Published Documents


TOTAL DOCUMENTS

18
(FIVE YEARS 2)

H-INDEX

4
(FIVE YEARS 0)

2021 ◽  
Vol 11 (1) ◽  
pp. 655-671
Author(s):  
Daniele Cassani ◽  
Antonio Tarsia

Abstract We first prove De Giorgi type level estimates for functions in W 1,t (Ω), Ω ⊂ R N $ \Omega\subset{\mathbb R}^N $ , with t > N ≥ 2 $ t \gt N\geq 2 $ . This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi’s classes as obtained in Di Benedetto–Trudinger [10] for functions in W 1,2(Ω). As a consequence, we prove the validity of the strong maximum principle for uniformly elliptic operators of any even order, in fairly general domains in dimension two and three, provided second order derivatives are taken into account.



2020 ◽  
Vol 28 (4) ◽  
pp. 281-290
Author(s):  
Brahim Boufoussi ◽  
Soufiane Mouchtabih

AbstractUsing the coupling method and Girsanov theorem, we prove a Harnack-type inequality for a stochastic differential equation with non-Lipschitz drift and driven by a fractional Brownian motion with Hurst parameter {H<\frac{1}{2}}. We also investigate this inequality for a stochastic differential equation driven by an additive fractional Brownian sheet.





2019 ◽  
Vol 31 (4) ◽  
pp. 1007-1026 ◽  
Author(s):  
Ewa Damek ◽  
Zeineb Ghardallou

Abstract Let {\mathcal{L}} be the Laplace operator on {\mathbb{R}^{d}} , {d\geq 3} , or the Laplace–Beltrami operator on the harmonic NA group (in particular, on a rank one noncompact symmetric space). For the equation {\mathcal{L}u-\varphi(\,\cdot\,,u)=0} we give necessary and sufficient conditions for the existence of entire bounded or large solutions under the hypothesis of radiality of φ with respect to the first variable. A Harnack-type inequality for positive continuous solutions is also proved.



2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Mathew R. Gluck ◽  
Ying Guo ◽  
Lei Zhang

AbstractIn this paper the method of moving spheres is used to derive a Harnack-type inequality for positive solutions ofwhere n ≥ 4, ℝ.



2012 ◽  
Vol 62 (4) ◽  
Author(s):  
Jiaqing Pan

AbstractThe geometric character of domains of solutions of a singular parabolic equation with the Neumann boundary condition are discussed in this work. We prove a gradient estimate and a Harnack type inequality and then, show that the domains of the solutions are exactly columns in the space-time. Specially, the altitudes of the columns are calculated accurately.



Sign in / Sign up

Export Citation Format

Share Document