Zobrazeno 1 - 10
of 198
pro vyhledávání: '"Zhou, Xiaodan"'
This paper is concerned with a PDE approach to horizontally quasiconvex (h-quasiconvex) functions in the Heisenberg group based on a nonlinear second order elliptic operator. We discuss sufficient conditions and necessary conditions for upper semicon
Externí odkaz:
http://arxiv.org/abs/2312.10364
We study the asymptotic behavior of three classes of nonlocal functionals in complete metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. We show that the limits of these nonlocal functionals are comparable to the v
Externí odkaz:
http://arxiv.org/abs/2310.08882
Autor:
Liu, Qing, Zhou, Xiaodan
These are lecture notes for our minicourse at OIST Summer Graduate School "Analysis and Partial Differential Equations" on June 12-17, 2023. We give an overview and collect a few important results concerning the well-posedness of Hamilton-Jacobi equa
Externí odkaz:
http://arxiv.org/abs/2308.08073
In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely $p$-integrable in the domain with a finite $p$. For continuous eikonal equations, it is known tha
Externí odkaz:
http://arxiv.org/abs/2308.06872
We study existence and uniqueness of Green functions for the Cheeger $Q$-Laplacian in metric measure spaces that are Ahlfors $Q$-regular and support a $Q$-Poincar\'e inequality with $Q>1$. We prove uniqueness of Green functions both in the case of re
Externí odkaz:
http://arxiv.org/abs/2211.11974
Autor:
Lahti Panu, Zhou Xiaodan
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 12, Iss 1, Pp 554-577 (2024)
Given a homeomorphism f:X→Yf:X\to Y between QQ-dimensional spaces X,YX,Y, we show that ff satisfying the metric definition of quasiconformality outside suitable exceptional sets implies that ff belongs to the Sobolev class Nloc1,p(X;Y){N}_{{\rm{loc
Externí odkaz:
https://doaj.org/article/333a3c6c40444c1fad937e2869cf94a1
We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Compared with previous works, we consider more general functionals. We also giv
Externí odkaz:
http://arxiv.org/abs/2207.02488
This paper is concerned with a PDE-based approach to the horizontally quasiconvex (h-quasiconvex for short) envelope of a given continuous function in the Heisenberg group. We provide a characterization for upper semicontinuous, h-quasiconvex functio
Externí odkaz:
http://arxiv.org/abs/2205.01993
Autor:
Lahti, Panu, Zhou, Xiaodan
Following Mal\'y's definition of absolutely continuous functions of several variables, we consider $Q$-absolutely continuous mappings $f\colon X\to V$ between a doubling metric measure space $X$ and a Banach space $V$. The relation between these mapp
Externí odkaz:
http://arxiv.org/abs/2109.13615
Autor:
Lahti, Panu, Zhou, Xiaodan
Given a homeomorphism $f\colon X\to Y$ between $Q$-dimensional spaces $X,Y$, we show that $f$ satisfying the metric definition of quasiconformality outside suitable exceptional sets implies that $f$ belongs to the Sobolev class $N_{\rm{loc}}^{1,p}(X;
Externí odkaz:
http://arxiv.org/abs/2109.01260