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
Author(s):  
Francesca Gladiali ◽  
Massimo Grossi

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.


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

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

2020 ◽  
Vol 53 (2) ◽  
pp. 9256-9261
Author(s):  
Alexey Matveev ◽  
Alexander Kapitonov ◽  
Ivan Berman ◽  
Valerii Chernov

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