Growth in the Muskat problem Page 1 Math. Model. Nat. Phenom. 15 (2020) 7 Mathematical
Modelling of Natural Phenomena https://doi.org/10.1051/mmnp/2019021 www.mmnp-journal.org …

We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli
problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a …

In this work we demonstrate that a class of some one and two phase free boundary
problems can be recast as nonlocal parabolic equations on a submanifold. The canonical …

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We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a
two-dimensional inhomogeneous porous media. The permeability of the porous medium is …

We establish that the C 1, γ regularity theory for translation invariant fractional order
parabolic integro-differential equations (via Krylov-Safonov estimates) gives an …

In this article, we apply the viscosity solutions theory for integro-differential equations to
the\emph {one-phase} Muskat equation (also known as the Hele-Shaw problem with …

We study the regularity of the free boundary in one-phase Stefan problem with nonlinear
operator. Using the Hodograph transform and a linearization technique, we prove that flat …

ut=∆ u in (Ω×(0, T])∩{u> 0}, ut=|∇ u| 2 su (Ω×(0, T])∩∂{u> 0}, con Ω⊂ Rn, u: Ω×[0, T]→ R,
u≥ 0. Incominciamo richiamando i risultati classici ottenuti da I. Athanasopoulos, L …

In this note, we discuss about the regularity of the free boundary for the solutions of the one-
phase Stefan problem. We start by recalling the classical results achieved by I …