6533b837fe1ef96bd12a3220
RESEARCH PRODUCT
Mappings of finite distortion: discreteness and openness for quasi-light mappings
Stanislav HenclPekka Koskelasubject
CombinatoricsDistortion (mathematics)Open mappingApplied MathematicsHausdorff dimensionMathematical analysisFunction (mathematics)Mathematical PhysicsAnalysisMathematicsdescription
Abstract Let f ∈ W 1 , n ( Ω , R n ) be a continuous mapping so that the components of the preimage of each y ∈ R n are compact. We show that f is open and discrete if | D f ( x ) | n ⩽ K ( x ) J f ( x ) a.e. where K ( x ) ⩾ 1 and K n − 1 / Φ ( log ( e + K ) ) ∈ L 1 ( Ω ) for a function Φ that satisfies ∫ 1 ∞ 1 / Φ ( t ) d t = ∞ and some technical conditions. This divergence condition on Φ is shown to be sharp.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-05-01 | Annales de l'Institut Henri Poincaré C, Analyse non linéaire |