6533b861fe1ef96bd12c45a0

RESEARCH PRODUCT

Invertibility of Sobolev mappings under minimal hypotheses

Kai RajalaLeonid V. KovalevJani Onninen

subject

Sobolev spaceInverse function theoremDiscrete mathematicsDistortion functionDifferential inclusionIntegrable systemApplied MathematicsLocal homeomorphismDifferentiable functionHomeomorphismMathematical PhysicsAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2010-04-01Annales de l'Institut Henri Poincare (C) Non Linear Analysis
10.1016/j.anihpc.2009.09.010http://dx.doi.org/10.1016/j.anihpc.2009.09.010