1 citations · 1 across the 6 of their papers we have counts for
7 papers
Absolutely continuous mappings on doubling metric measure spaces
Panu Lahti, Xiaodan Zhou
Following Malý's definition of absolutely continuous functions of several variables, we consider -absolutely continuous mappings between a doubling metric measu…
Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces
Panu Lahti, Xiaodan Zhou
We show that a mapping satisfying the metric condition of quasiconformality outside suitable exceptional sets is in the Newton-Sobolev class $N_{\textrm{loc}}^{1,1…
Equivalence of solutions of eikonal equation in metric spaces
Qing Liu, Nageswari Shanmugalingam, Xiaodan Zhou
In this paper we prove the equivalence between some known notions of solutions to the eikonal equation and more general analogs of the Hamilton-Jacobi equations in complete and rec…
Functions of bounded variation on complete and connected one-dimensional metric spaces
Panu Lahti, Xiaodan Zhou
In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a c…
Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations
Qing Liu, Xiaodan Zhou
This paper introduces in a natural way a notion of horizontal convex envelopes of continuous functions in the Heisenberg group. We provide a convexification process to find the env…
Strong Comparison Principle for harmonic functions in Carnot-Caratheodory spaces
Luca Capogna, Xiaodan Zhou
We extend Bony's propagation of support argument \cite{Bony} to solutions of the non-homogeneous sub-elliptic Laplacian associated to a system of smooth vector fields sat…