A counterexample for pointwise upper bounds on Green's function with a singular drift at boundary

2024/05/22 by Pathak, Aritro · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.13313

Abstract

We show an example of a sequence of elliptic operators in the unit ball with drifts that diverge as the inverse distance to the boundary, for which we don't get uniform upper estimates for the Green's function with the pole at the origin. Such drifts have been considered in the literature in the study of the L^p Dirichlet problem for both the parabolic and elliptic operators.

Cited by

• The doubling property of the elliptic measure, for elliptic operators with drifts satisfying an average diverging condition
• Pointwise bounds on Dirichlet Green's functions for a singular drift term

Related

• Pointwise bounds on Dirichlet Green's functions for a singular drift term
• The doubling property of the elliptic measure, for elliptic operators with drifts satisfying an average diverging condition
• Carleson estimates for the Green function on domains with lower dimensional boundaries
• A stability result for parabolic measures of operators with singular drifts
• Green's function for elliptic systems: moment bounds