TY - JOUR
T1 - Regularity of the free boundary for a parabolic cooperative system
AU - Aleksanyan, G.
AU - Fotouhi, M.
AU - Shahgholian, H.
AU - Weiss, G. S.
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/8
Y1 - 2022/8
N2 - In this paper we study the following parabolic system Δu-∂tu=|u|q-1uχ{|u|>0},u=(u1,⋯,um),with free boundary ∂{ | u| > 0 }. For 0 ≤ q< 1 , we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C1,α in space directions and half-Lipschitz in the time direction.
AB - In this paper we study the following parabolic system Δu-∂tu=|u|q-1uχ{|u|>0},u=(u1,⋯,um),with free boundary ∂{ | u| > 0 }. For 0 ≤ q< 1 , we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C1,α in space directions and half-Lipschitz in the time direction.
UR - https://www.scopus.com/pages/publications/85129534949
U2 - 10.1007/s00526-022-02244-1
DO - 10.1007/s00526-022-02244-1
M3 - Article
AN - SCOPUS:85129534949
SN - 0944-2669
VL - 61
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 4
M1 - 124
ER -