Isometric immersion in E3 of a convex domain of the Lobachevskii plane containing two horocircles

1986 ◽  
Vol 39 (4) ◽  
pp. 335-338 ◽  
Author(s):  
Zh. Kaidasov ◽  
E. V. Shikin
Keyword(s):  
Convex Domain ◽  
Isometric Immersion ◽  
Lobachevskii Plane

scholarly journals Strichartz estimates for the wave equation on a 2D model convex domain

2021 ◽  
Vol 300 ◽  
pp. 830-880
Author(s):  
Oana Ivanovici ◽  
Gilles Lebeau ◽  
Fabrice Planchon
Keyword(s):  
Wave Equation ◽  
Convex Domain ◽  
Strichartz Estimates ◽  
2D Model

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.

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