The existence of k-convex hypersurface with prescribed mean curvature

Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Calculus of variations and partial differential equations 2011-09, Vol.42 (1-2), p.43-72
Hauptverfasser:	Han, Fei, Ma, Xi-Nan, Wu, Damin
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Calculus Calculus of variations Calculus of Variations and Optimal Control Optimization Control Curvature Existence theorems Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Maximum principle Partial differential equations Systems Theory Theorems Theoretical
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .
ISSN:	0944-2669 1432-0835
DOI:	10.1007/s00526-010-0379-2