A Self-Dual Polar Factorization for Vector Fields
نویسندگان
چکیده
منابع مشابه
A Self-dual Polar Factorization for Vector Fields
We show that any non-degenerate vector field u in L∞(Ω,RN), where Ω is a bounded domain in RN , can be written as u(x) = ∇1H(S(x),x) for a.e. x ∈Ω, where S is a measure preserving point transformation on Ω such that S2 = I a.e (an involution), and H : RN ×RN → R is a globally Lipschitz anti-symmetric convex-concave Hamiltonian. Moreover, u is a monotone map if and only if S can be taken to be t...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2012
ISSN: 0010-3640
DOI: 10.1002/cpa.21430