6533b7d0fe1ef96bd125b020
RESEARCH PRODUCT
Mappings of Lp-integrable distortion: regularity of the inverse
Jani OnninenVille Tengvallsubject
regularity of the inverseUnit sphereDistortion functionDiscrete mathematicsPure mathematicsSobolev homeomorphismGeneral Mathematicsta111010102 general mathematicsOpen setInverse01 natural sciencesModulus of continuityHomeomorphism010101 applied mathematicsSobolev spaceDistortion (mathematics)mappings of finite distortionmodulus of continuityhigher integrability0101 mathematicsMathematicsdescription
Let be an open set in ℝn and suppose that is a Sobolev homeomorphism. We study the regularity of f–1 under the Lp-integrability assumption on the distortion function Kf. First, if is the unit ball and p > n – 1, then the optimal local modulus of continuity of f–1 is attained by a radially symmetric mapping. We show that this is not the case when p ⩽ n – 1 and n ⩾ 3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for ∣Df–1∣ in terms of the Lp-integrability assumptions of Kf.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-05-16 | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |