TY - JOUR
T1 - Convexity of the free boundary for an exterior free boundary problem involving the perimeter
AU - Mikayelyan, Hayk
AU - Shahgholian, Henrik
PY - 2013/5
Y1 - 2013/5
N2 - We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫BR |∇v|pdx + Per({v > 0}), 1 < p < ∞ over the set {v ∈ W0 1,p(BR)|v ≡ 1 on K ⊂ BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.
AB - We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫BR |∇v|pdx + Per({v > 0}), 1 < p < ∞ over the set {v ∈ W0 1,p(BR)|v ≡ 1 on K ⊂ BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.
KW - Free boundary problems
KW - Mean curvature
UR - http://www.scopus.com/inward/record.url?scp=84873316680&partnerID=8YFLogxK
U2 - 10.3934/cpaa.2013.12.1431
DO - 10.3934/cpaa.2013.12.1431
M3 - Article
AN - SCOPUS:84873316680
SN - 1534-0392
VL - 12
SP - 1431
EP - 1443
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 3
ER -