BMO solvability with singular drifts on ample sawtooth domains implies L^p solvability

2025/11/16 by Pathak, Aritro
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.12747

Abstract

For a linear elliptic operator with a singular drift that satisfies a finite Carleson measure condition, we prove that there exist `ample' sawtooth domains of the unit ball B(0,1)⊂ \R<sup>n+1</sup> so that a BMO solvability assumption in these sawtooth subdomains implies that the elliptic measure satisfies the weak A_∞ condition with respect to the surface measure on this `ample' sawtooth domain. This is a quantifiable absolute continuity condition, which is equivalent to saying the L^p Dirichlet problem is solvable for some 1

Citations

• The Dirichlet Problem for elliptic equations with singular drift terms
• Boundary value problems for elliptic operators satisfying Carleson condition
• BMO solvability and absolute continuity of harmonic measure
• BMO solvability and the A_∞ condition for elliptic operators
• Carleson measures, trees, extrapolation, and T(b) theorems

Related

• BMO solvability and the A_∞ condition for elliptic operators
• The Dirichlet Problem for elliptic equations with singular drift terms
• BMO solvability and absolute continuity of harmonic measure
• The doubling property of the elliptic measure, for elliptic operators with drifts satisfying an average diverging condition
• Carleson perturbations of locally Lipschitz elliptic operators