caa a22 4500 445843616 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00526-010-0333-3 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0333-3 Xu Lu Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 430071, Wuhan, People's Republic of China aut A microscopic convexity theorem of level sets for solutions to elliptic equations [Elektronische Daten] [Lu Xu] We study the microscopic level-set convexity theorem for elliptic equation Lu=f(x, u, Du), which generalize Korevaars' result in (Korevaar, Commun Part Diff Eq 15(4):541-556, 1990) by using different expression for the elementary symmetric functions of the principal curvatures of the level surface. We find out that the structure conditions on equation are as same as conditions in macroscopic level-set convexity results (see e.g. (Colesanti and Salani, Math Nachr 258:3-15, 2003; Greco, Bound Value Prob 1-15, 2006)). In a forthcoming paper, we use the same techniques to deal with Hessian type equations. Springer-Verlag, 2010 Calculus of Variations and Partial Differential Equations Springer-Verlag 40/1-2(2011-01-01), 51-63 0944-2669 40:1-2<51 2011 40 526 https://doi.org/10.1007/s00526-010-0333-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0333-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Xu Lu Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 430071, Wuhan, People's Republic of China aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 40/1-2(2011-01-01), 51-63 0944-2669 40:1-2<51 2011 40 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer