Search results for "Local homeomorphism"

showing 2 items of 2 documents

On BLD-mappings with small distortion

2021

We show that every $$L$$ -BLD-mapping in a domain of $$\mathbb {R}^{n}$$ is a local homeomorphism if $$L < \sqrt{2}$$ or $$K_I(f) < 2$$ . These bounds are sharp as shown by a winding map.

Pure mathematicsPartial differential equationFunctional analysisMathematics - Complex VariablesLocal homeomorphismBLD-mappings010102 general mathematicsbranch setA domain30C65 57M12 30L10quasiregular mappingsMetric Geometry (math.MG)General MedicineAlgebraic geometry01 natural scienceslocal homeomorphismMathematics::Geometric TopologyDistortion (mathematics)010104 statistics & probabilityMathematics - Metric Geometry111 MathematicsFOS: Mathematics0101 mathematicsComplex Variables (math.CV)Mathematics
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Invertibility of Sobolev mappings under minimal hypotheses

2010

Abstract We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W 1 , n mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.

Sobolev spaceInverse function theoremDiscrete mathematicsDistortion functionDifferential inclusionIntegrable systemApplied MathematicsLocal homeomorphismDifferentiable functionHomeomorphismMathematical PhysicsAnalysisMathematicsAnnales de l'Institut Henri Poincare (C) Non Linear Analysis
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