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math.AP2021★ 1 cited
Quantitative homogenization for the obstacle problem and its free boundary
Gohar Aleksanyan, Tuomo Kuusi
In this manuscript we prove quantitative homogenization results for the obstacle problem with bounded measurable coefficients. As a consequence, large-scale regularity results both…
math.AP2021
Regularity of the free boundary for a parabolic cooperative system
Gohar Aleksanyan, Morteza Fotouhi, Henrik Shahgholian +1
In this paper we study the following parabolic system \begin{equation*} Δ\u -\partial_t \u =|\u|^{q-1}\u\,χ_{\{ |\u|>0 \}}, \qquad \u = (u^1, \cdots , u^m) \ , \end{equation*} with…