showing 4 related works from this author
Mappings of Finite Distortion:¶Discreteness and Openness
2001
We establish a sharp integrability condition on the partial derivatives of a mapping with L p -integrable distortion for some p>n− 1 to guarantee discreteness and openness. We also show that a mapping with exponentially integrable distortion and integrable Jacobian determinant is either constant or both discrete and open. We give an example demonstrating the preciseness of our criterion.
On functions with derivatives in a Lorentz space
1999
We establish a sharp integrability condition on the partial derivatives of a Sobolev mapping to guarantee that sets of measure zero get mapped to sets of measure zero. This condition is sharp also for continuity and differentiability almost everywhere.
Mappings of finite distortion: Sharp Orlicz-conditions
2003
We establish continuity, openness and discreteness, and the condition $(N)$ for mappings of finite distortion under minimal integrability assumptions on the distortion.
An example concerning the zero set of the Jacobian
2006
AbstractLet f∈W1,1(Ω,Rn) be a homeomorphism of finite distortion K. It is known that if K1/(n−1)∈L1(Ω), then the Jacobian Jf of f is positive almost everywhere in Ω. We will show that this integrability assumption on K is sharp in any Orlicz-scale: if α is increasing function (satisfying minor technical assumptions) such that limt→∞α(t)=∞, then there exists f such that K1/(n−1)/α(K)∈L1(Ω) and Jf vanishes in a set of positive measure.