scholarly journals Improving L 2 estimates to Harnack inequalities

2009 ◽  
Vol 99 (2) ◽  
pp. 326-352 ◽  
Author(s):  
Stathis Filippas ◽  
Luisa Moschini ◽  
Achilles Tertikas
Keyword(s):  
Harnack Inequalities

scholarly journals Measure Estimates, Harnack Inequalities and Ricci Lower Bound

2018 ◽  
Vol 55 ◽  
pp. 21-51
Author(s):  
Yu Wang ◽  
Xiangwen Zhang
Keyword(s):  
Lower Bound ◽  
Harnack Inequalities

scholarly journals Integrated Harnack inequalities on Lie groups

2009 ◽  
Vol 83 (3) ◽  
pp. 501-550 ◽  
Author(s):  
Bruce K. Driver ◽  
Maria Gordina
Keyword(s):  
Lie Groups ◽  
Harnack Inequalities

Harnack inequalities and applications for functional SDEs driven by fractional Brownian motion

2014 ◽  
Vol 22 (4) ◽  
Author(s):  
Zhi Li ◽  
Jiaowan Luo
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Functional Differential Equations ◽  
Hurst Parameter ◽  
Stochastic Functional Differential Equations ◽  
Harnack Inequalities ◽  
Functional Differential ◽  
Stochastic Functional

AbstractIn this paper, Harnack inequalities are established for stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter

scholarly journals The asymptotic Dirichlet problems on manifolds with unbounded negative curvature

2018 ◽  
Vol 167 (01) ◽  
pp. 133-157
Author(s):  
RAN JI
Keyword(s):  
Dirichlet Problem ◽  
Negative Curvature ◽  
Probabilistic Method ◽  
Martin Boundary ◽  
Dirichlet Problems ◽  
Curvature Condition ◽  
New Approach ◽  
Harnack Inequalities ◽  
Geometric Boundary ◽  
Analytical Proof

AbstractElton P. Hsu used probabilistic method to show that the asymptotic Dirichlet problem is uniquely solvable under the curvature condition −Ce(2−η)r(x) ≤ KM(x) ≤ −1 with η > 0. We give an analytical proof of the same statement. In addition, using this new approach we are able to establish two boundary Harnack inequalities under the curvature condition −Ce(2/3−η)r(x) ≤ KM(x) ≤ −1 with η > 0. This implies that there is a natural homeomorphism between the Martin boundary and the geometric boundary of M. As far as we know, this is the first result of this kind under unbounded curvature conditions. Our proof is a modification of an argument due to M. T. Anderson and R. Schoen.

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