Can I read Non-existence of cusps for degenerate Alt-Caffarelli functionals on EtoBox?

Non-existence of cusps for degenerate Alt-Caffarelli functionals by McCurdy, Sean; Naples, Lisa is a scholarly article available to read on EtoBox.

What is Non-existence of cusps for degenerate Alt-Caffarelli functionals about?

We eliminate the existence of cusps in a class of \textit{degenerate} free-boundary problems for the Alt-Caffarelli functional $J_{Q}(v, \Omega):= \int_{\Omega}|\nabla v|^2 + Q^2(x)\chi_{\{v>0\}}dx,$ so-called because $Q(x) = \text{dist}(x, \Gamma)^{\gamma}$ for $\Gamma$ an affine $k$-plane and $0< \gamma$. This problem is inspired by a generalization of the variational formulation of the Stokes Wave by Arama and Leoni. The elimination of cusps implies that the results of [Mccurdy20] in fact describe the entire free-boundary as it intersects $\Gamma$.

Author

McCurdy, Sean; Naples, Lisa

Published

2022

Language

EN