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A remark on N. Korevaar's concavity maximum principle and on the asymptotic uniqueness of solutions to the plasma problem
Author(s) -
Kawohl B.,
Payne L.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080107
Subject(s) - mathematics , uniqueness , maximum principle , regular polygon , boundary value problem , function (biology) , mathematical analysis , convex analysis , convex function , boundary (topology) , pure mathematics , convex optimization , mathematical optimization , geometry , optimal control , evolutionary biology , biology
Recently N. Korevaar developed a method of proving that solutions to elliptic and parabolic boundary value problems on convex domains ω ⊂ R n are convex functions. He introduced a concavity functionand used the classical maximum principle to prove that C ⩾ 0 on ω × ω, i.e. that u is convex. Both he and independently L. Caffarelli and J. Spruck applied this method successfully to various boundary value problems. In this note we weaken the assumptions of their theorems and obtain some interesting new applications which are not covered by their previous results [CS, Ko].