A microscopic convexity principle for nonlinear partial differential equations

• 成果类型: Article
• 署名作者: Bian, Baojun; Guan, Pengfei
• 署名单位: McGill University; Tongji University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0179-5
• 发表日期: 2009
• 页码: 307-335
• 关键词: boundary-value-problems; elliptic-equations; weingarten curvature; mean-curvature; minkowski; hypersurfaces; SURFACES; FLOW

摘要

We study microscopic convexity property of fully nonlinear elliptic and parabolic partial differential equations. Under certain general structure condition, we establish that the rank of Hessian a double dagger (2) u is of constant rank for any convex solution u of equation F(a double dagger (2) u,a double dagger u,u,x)=0. The similar result is also proved for parabolic equations. Some of geometric applications are also discussed.