12 citations · 17 across the 11 of their papers we have counts for
12 papers
Extensions and approximations of Banach-valued Sobolev functions
Miguel García-Bravo, Toni Ikonen, Zheng Zhu
In complete metric measure spaces equipped with a doubling measure and supporting a weak Poincaré inequality, we investigate when a given Banach-valued Sobolev function defined on…
Zero volume boundary for extension domains from Sobolev to
Tapio Rajala, Zheng Zhu
In this note, we prove that the boundary of a -extension domain is of volume zero under the assumption that the domain $\boz$ is -fat at almost every $x\in\parti…
The extension property for domains with one singular point
Pekka Koskela, Zheng Zhu
An arbitrary outward cuspidal domain is shown to be bi-Lipschitz equivalent to a Lipschitz outward cuspidal domain via a global transformation. This allows us to extend earlier Sob…
Bi-Lipschitz invariance of planar - and -extension domains
Miguel García-Bravo, Tapio Rajala, Zheng Zhu
We prove that a bi-Lipschitz image of a planar -extension domain is also a -extension domain, and that a bi-Lipschitz image of a planar -extension domain is again…
Sobolev Extension on -Quasidisks
Zheng Zhu
In this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of the classical quasidisks. After that, we also find some applications of the…
Pointwise inequalities for Sobolev functions on generalized cuspidal domains
Zheng Zhu
We establish point wise inequalities for Sobolev functions on a wider class of outward cuspidal domains. It is a generalization of an earlier result by the author and his collabora…
The volume of the boundary of a Sobolev -extension domain
Pekka Koskela, Alexander Ukhlov, Zheng Zhu
Let and $1\leq q<p<\fz$. We prove that if is a Sobolev -extension domain, with additional capacitory restrictions on boundary in the case $q…
Pointwise inequalities for Sobolev functions on outward cuspidal domains
Sylvester Eriksson-Bique, Pekka Koskela, Jan Maly +1
We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spa…
Singularities In L p-quasidisks
Tadeusz Iwaniec, Jani Onninen, Zheng Zhu
We study planar domains with exemplary boundary singularities of the form of cusps. A natural question is how much elastic energy is needed to flatten these cusps; that is, to remo…
Creating and Flattening Cusp Singularities by Deformations of Bi-conformal Energy
Tadeusz Iwaniec, Jani Onninen, Zheng Zhu
Mappingsofbi-conformalenergyformthewidestclass of homeomorphisms that one can hope to build a viable extension of Geometric Function Theory with connections to mathematical models…
Deformations of Bi-conformal Energy and a new Characterization of Quasiconformality
Tadeusz Iwaniec, Jani Onninen, Zheng Zhu
The concept of hyperelastic deformations of bi-conformal energy is developed as an extension of quasiconformality. These are homeomorphisms between domains $ X, Y \subs…
Product of extension domains is still an extension domain
Pekka Koskela, Zheng Zhu
We prove the product of the Sobolev-extension domains is still a Sobolev-extension domain.