کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9518228 1345536 2005 43 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations
چکیده انگلیسی
In dimension n⩾3, we define a generalization of the classical two-dimensional partial Legendre transform, that reduces interior regularity of the generalized Monge-Ampère equation detD2u=k(x,u,Du) to regularity of a divergence form quasilinear system of special form. This is then used to obtain smoothness of C2,1 solutions, having n-1 nonvanishing principal curvatures, to certain subelliptic Monge-Ampère equations in dimension n⩾3. A corollary is that if k⩾0 vanishes only at nondegenerate critical points, then a C2,1 convex solution u is smooth if and only if the symmetric function of degree n-1 of the principal curvatures of u is positive, and moreover, u fails to be C3,1-2n+ɛ when not smooth.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 193, Issue 2, 1 June 2005, Pages 373-415
نویسندگان
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