ﻻ يوجد ملخص باللغة العربية
We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more generally for minimizers of the Alt-Phillips functional.
Given a global 1-homogeneous minimizer $U_0$ to the Alt-Caffarelli energy functional, with $sing(F(U_0)) = {0}$, we provide a foliation of the half-space $R^{n} times [0,+infty)$ with dilations of graphs of global minimizers $underline U leq U_0 leq
For a vectorial Bernoulli-type free boundary problem, with no sign assumption on the components, we prove that flatness of the free boundary implies $C^{1,alpha}$ regularity, as well-known in the scalar case cite{AC,C2}. While in cite{MTV2} the same
We show how the Stefan type free boundary problem with random diffusion in one space dimension can be approximated by the corresponding free boundary problem with nonlocal diffusion. The approximation problem is a slightly modified version of the non
This is an introduction to The Theme Issue on Free Boundary Problems and Related Topics, which consists of 14 survey/review articles on the topics, of Philosophical Transactions of the Royal Society A: Physical, Mathematical and Engineering Sciences, 373, no. 2050, The Royal Society, 2015.
The semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove existence of solutions of the incompressible semi-geostrophic equations in a fully three-dimensional domain with a free upper bounda