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math.AP2026
Singular set estimates for solutions to elliptic equations in higher co-dimension
Max Engelstein, Cole Jeznach, Yannick Sire
Recent advances in quantitative unique continuation properties for solutions to uniformly elliptic, divergence form equations (with Lipschitz coefficients) has led to a good unders…
math.AP2025
Regularity of the free boundary for the supercooled Stefan problem in arbitrary dimensions
Max Engelstein, Inwon Kim, Sebastian Munoz
We study the free boundary in the supercooled Stefan problem, a classical model for the solidification of water below its freezing temperature. In contrast with the melting problem…
math.AP2025
On the asymptotic properties of solutions to one-phase free boundary problems
Max Engelstein, Daniel Restrepo, Zihui Zhao
In this article we study the structure of solutions to the one-phase Bernoulli problem that are modeled either infinitesimally or at infinity by one-homogeneous solutions with an i…