On the boundedness of first derivatives for solutions to the Neumann–Laplace problem in a convex domain

2009 ◽  
Vol 159 (1) ◽  
pp. 104-112 ◽  
Author(s):  
Vladimir Maz’ya
Keyword(s):  
Convex Domain ◽  
Laplace Problem

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.

scholarly journals A Random String with Reflection in a Convex Domain

2011 ◽  
Vol 29 (3) ◽  
pp. 523-549 ◽  
Author(s):  
Said Karim Bounebache
Keyword(s):  
Convex Domain ◽  
Random String

scholarly journals The lower bound for the modulus of the derivatives and Jacobian of harmonic injective mappings

Filomat ◽  
2015 ◽  
Vol 29 (2) ◽  
pp. 221-244 ◽  
Author(s):  
Miodrag Mateljevic
Keyword(s):  
Lower Bound ◽  
Unit Ball ◽  
Convex Domain ◽  
Lipschitz Property ◽  
Planar Case

We give the lower bound for the modulus of the radial derivatives and Jacobian of harmonic injective mappings from the unit ball onto convex domain in plane and space. As an application we show co-Lipschitz property of some classes of qch mappings. We also review related results in planar case using some novelty.

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