The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-
phase free boundary problem. The problem of classifying stable (or minimal) homogeneous …

We study viscosity solutions to the classical one-phase problem and its thin counterpart. In
low dimensions, we show that when the free boundary is the graph of a continuous function …

The free boundary for the Signorini problem in R n+ 1 is smooth outside of a degenerate set,
which can have the same dimension (n− 1) as the free boundary itself. In [15] it was shown …

We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their
mean curvature flow encounters only spherical and cylindrical singularities. Our theorem …

We study the higher regularity of solutions and free boundaries in the Alt-Phillips problem
$\Delta u= u^{\gamma-1} $, with $\gamma\in (0, 1) $. Our main results imply that, once free …

We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli
functional (also known as Bernoulli free boundary problem) in the case of continuous and …

We investigate the structure of the nodal set of solutions to an unstable Alt-Philips type
problem-Δ u= λ+(u+) p-1-λ-(u-) q-1, where 1≤ p< q< 2, λ+> 0, λ-≥ 0. The equation is …

Regularity theory for obstacle problems and boundary Harnack inequalities Page 1 Regularity
theory for obstacle problems and boundary Harnack inequalities by Clara Torres Latorre PhD …

Regularity for the one-phase problem - Master Project in mathematics Page 1 Regularity for the
one-phase problem Master Project in mathematics Florian Noah Grün École Polytechnique …