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V=G-R_r^{\mathcal C}\Gamma, \] where the reflected diffusion is killed upon entry into the stopping set. This corrects the generally invalid unrestricted-resolvent formula. Under explicit monotonicity hypotheses, the stopping set has epigraph form, and the free boundary is characterized by a killed-potential trace condition. A verification theorem certifies locally Lipschitz candidate boundaries as optimal.
From: Louis Shuo Wang [view email]
[v1]
Fri, 19 Jun 2026 16:18:17 UTC (129 KB)
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