Abstract:In convex bounded domains in R^n with n >= 3, we establish interior pointwise upper bounds for the Dirichlet Green's function of elliptic operators in the unit ball B(0,1) in R^n, n >= 3, whose principal part is the Laplacian and which include a drift term that diverges near the boundary like a negative power of the distance with exponent strictly less than 1. This work extends an earlier result for operators with such drifts in the unit ball, and streamlines the proof in particular to adopt it to the question in convex domains.
From: Aritro Pathak [view email]
[v1]
Sun, 12 Apr 2026 12:58:33 UTC (100 KB)
[v2]
Sat, 20 Jun 2026 09:14:43 UTC (101 KB)
[v3]
Wed, 24 Jun 2026 08:39:00 UTC (102 KB)
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