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math.AP2022
Non-existence of cusps for a Free-boundary Problem for Water Waves
Sean McCurdy
In arXiv:0908.1031, Varvaruca and Weiss eliminate the existence of cusps for a free-boundary problem for two-dimensional water waves under assumptions that hold for solutions such…
math.AP2022
Non-existence of cusps for degenerate Alt-Caffarelli functionals
Sean McCurdy, Lisa Naples
We eliminate the existence of cusps in a class of \textit{degenerate} free-boundary problems for the Alt-Caffarelli functional $J_{Q}(v, Ω):= \int_Ω|\nabla v|^2 + Q^2(x)χ_{\{v>0\}}…