Behavior near the origin of f′(u⁎) in radial singular extremal solutions

2021 ◽  
Vol 270 ◽  
pp. 947-960
Author(s):  
Salvador Villegas
Keyword(s):  
Extremal Solutions ◽  
Singular Extremal

Extremal solutions of some constrained control problems∗

Optimization ◽  
1995 ◽  
Vol 35 (4) ◽  
pp. 345-355 ◽  
Author(s):  
H. X. Phu ◽  
H. G. Bock ◽  
J. P. Schölder
Keyword(s):  
Extremal Solutions ◽  
Control Problems ◽  
Constrained Control ◽  
Constrained Control Problems

Regularity of almost extremal solutions of Monge–Ampère equations

1991 ◽  
Vol 117 (1-2) ◽  
pp. 21-29 ◽  
Author(s):  
John I. E. Urbas
Keyword(s):  
Large Class ◽  
Convex Domain ◽  
Gauss Curvature ◽  
Extremal Solutions ◽  
Classical Solutions ◽  
Uniformly Convex ◽  
Suitable Sense ◽  
Monge Ampere

SynopsisWe show that for a large class of Monge-Ampère equations, generalised solutions on a uniformly convex domain Ω⊂ℝn are classical solutions on any pre-assigned subdomain Ω′⋐Ω, provided the solution is almost extremal in a suitable sense. Alternatively, classical regularity holds on subdomains of Ω which are sufficiently distant from ∂Ω. We also show that classical regularity may fail to hold near ∂Ω in the nonextremal case. The main example of the class of equations considered is the equation of prescribed Gauss curvature.

Sign in / Sign up

Export Citation Format

Share Document