The equivalence of strict convexity and injectivity of the gradient in bounded level sets

1991 ◽  
Vol 51 (1-3) ◽  
pp. 273-278 ◽  
Author(s):  
Andreas Griewank ◽  
Hubertus Th. Jongen ◽  
Man Kam Kwong
Keyword(s):  
Level Sets ◽  
Strict Convexity ◽  
Bounded Level Sets

Strict convexity of level sets of solutions of some nonlinear elliptic equations

2004 ◽  
Vol 134 (2) ◽  
pp. 363-373 ◽  
Author(s):  
Francesca Gladiali ◽  
Massimo Grossi
Keyword(s):  
Elliptic Equations ◽  
Level Sets ◽  
Nonlinear Elliptic Equations ◽  
Gauss Curvature ◽  
Strict Convexity ◽  
Critical Growth ◽  
Strictly Convex ◽  
Nonlinear Elliptic ◽  
Suitable Function ◽  
Image Position

In this paper we study the convexity of the level sets of solutions of the problem where f is a suitable function with subcritical or critical growth. Under some assumptions on the Gauss curvature of ∂Ω, we prove that the level sets of the solution of (0.1) are strictly convex.

Perfect level sets in many directions

1986 ◽  
Vol 12 (1) ◽  
pp. 176
Author(s):  
Malý
Keyword(s):  
Level Sets

LEVEL SETS OF A TYPICAL C n FUNCTION

1998 ◽  
Vol 24 (1) ◽  
pp. 83
Author(s):  
Darji ◽  
Morayne
Keyword(s):  
Level Sets

scholarly journals Gradient-Free Tracking of Unsteady Environmental Level Sets in Dynamic Environments by a Nonholonomic Robot

2020 ◽  
Vol 53 (2) ◽  
pp. 9256-9261
Author(s):  
Alexey Matveev ◽  
Alexander Kapitonov ◽  
Ivan Berman ◽  
Valerii Chernov
Keyword(s):  
Level Sets ◽  
Dynamic Environments ◽  
Environmental Level
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