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math.AP2025
The doubling property of the elliptic measure, for elliptic operators with drifts satisfying an average diverging condition
Aritro Pathak
We show doubling of the elliptic measure corresponding to the operator with an elliptic principal term and a drift that diverges, on average on Whitney cubes, like the inverse dist…
math.AP2025
BMO solvability with singular drifts on ample sawtooth domains implies solvability
Aritro Pathak
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)…
math.AP2025
Pointwise bounds on Dirichlet Green's functions for a singular drift term
Aritro Pathak
We introduce a technique to obtain pointwise upper and lower bounds for the Green's function of elliptic operators whose principal part is the Laplacian and that include a drift te…