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math.AP2023
Asymptotic expansions for harmonic functions at conical boundary points
Dennis Kriventsov, Zongyuan Li
We prove three theorems about the asymptotic behavior of solutions to the homogeneous Dirichlet problem for the Laplace equation at boundary points with tangent cones. First, u…
math.AP2023
Rectifiability, finite Hausdorff measure, and compactness for non-minimizing Bernoulli free boundaries
Dennis Kriventsov, Georg S. Weiss
While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less in known…