Convexity of the free boundary in a filtration problem
نویسندگان
چکیده
منابع مشابه
Convexity of the Free Boundary for an Exterior Free Boundary Problem Involving the Perimeter
We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫ BR |∇v|dx + Per({v > 0}), 1 < p < ∞, over the set {v ∈ H 0 (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.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1981
ISSN: 0022-0396
DOI: 10.1016/0022-0396(81)90032-2