[HTML][HTML] Compact contact sets of sub-quadratic solutions to the thin obstacle problem

S Eberle, H Yu - Advances in Mathematics, 2024 - Elsevier
We study global solutions to the thin obstacle problem with at most quadratic growth at
infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On …

Free boundary partial regularity in the thin obstacle problem

F Franceschini, J Serra - Communications on Pure and Applied …, 2024 - Wiley Online Library
For the thin obstacle problem in R n R^n, n≥ 2 n≥2, we prove that at all free boundary
points, with the exception of a (n− 3) (n-3)‐dimensional set, the solution differs from its blow …

An epiperimetric inequality for odd frequencies in the thin obstacle problem

M Carducci, B Velichkov - arXiv preprint arXiv:2409.12110, 2024 - arxiv.org
We prove an epiperimetric inequality for the thin obstacle Weiss' energy with odd
frequencies and we apply it to solutions to the thin obstacle problem with general …

Free boundary regularity in the multiple membrane problem in the plane

O Savin, H Yu - Journal für die reine und angewandte Mathematik …, 2023 - degruyter.com
Free boundary regularity in the multiple membrane problem in the plane Skip to content Should
you have institutional access? Here's how to get it ... De Gruyter € EUR - Euro £ GBP - Pound …

2D Thin obstacle problem with data at infinity

R Lyu, Z Ye - arXiv preprint arXiv:2201.01465, 2022 - arxiv.org
In this paper, we consider the thin obstacle problem in $\mathbb {R}^ 2$ with data at infinity.
We first prove the existence and uniqueness of it. Then we show that its symmetric solutions …