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Regularity of a free boundary determined by the value of the gradient. Part 1: Third order asymptotics
This is the first part of a project concerning the regularity of the free boundary of a function, where the free boundary depends on the gradient of the function. We study the minimizer of the expression \begin{equation*} J(u) : = \int_{B_1} F(\nabla u) \ dx, \end{equation*} where $F(x)$ is a unif
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