Zobrazeno 1 - 10
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pro vyhledávání: '"Lahti, Panu"'
Autor:
Lahti, Panu
We define a relaxed version $H_f^{\textrm{fine}}$ of the distortion number $H_f$ that is used to define quasiconformal mappings. Then we show that for a BV function $f\in BV(\mathbb{R}^n;\mathbb{R}^n)$, for $|Df|$-a.e. $x\in\mathbb{R}^n$ it holds tha
Externí odkaz:
http://arxiv.org/abs/2406.05824
Autor:
Lahti, Panu, Nguyen, Khanh
In this paper, we study the existence of limits at infinity along almost every infinite curve for the upper and lower approximate limits of bounded variation functions on complete unbounded metric measure spaces. We prove that if the measure is doubl
Externí odkaz:
http://arxiv.org/abs/2404.09489
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:
Lahti, Panu
We study a class of non-local functionals that was introduced by Brezis-Seeger-Van Schaftingen-Yung (2022), and can be used to characterize functions of bounded variation. We give a new lower bound for the liminf of these functionals, involving the t
Externí odkaz:
http://arxiv.org/abs/2310.03550
Autor:
Lahti, Panu, Nguyen, Quoc-Hung
We study the BMO-type functional $\kappa_{\varepsilon}(f,\mathbb R^n)$, which can be used to characterize BV functions $f\in BV(\mathbb R^n)$. The $\Gamma$-limit of this functional, taken with respect to $L^1_{\mathrm{loc}}$-convergence, is known to
Externí odkaz:
http://arxiv.org/abs/2308.16543
Autor:
Lahti, Panu
We investigate a version of Alberti's rank one theorem in Ahlfors regular metric spaces, as well as a connection with quasiconformal mappings. More precisely, we give a proof of the rank one theorem that partially follows along the usual steps, but t
Externí odkaz:
http://arxiv.org/abs/2303.09157
Autor:
Lahti, Panu
We introduce a relaxed version of the metric definition of quasiconformality that is natural also for mappings of low regularity, including $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^n;\mathbb{R}^n)$-mappings. Then we show on the plane that this relaxed defi
Externí odkaz:
http://arxiv.org/abs/2211.12802
Autor:
Lahti, Panu
In a complete metric space equipped with a doubling measure and supporting a $(1,1)$-Poincar\'e inequality, we show that every set satisfying a suitable capacitary density condition is removable for Newton-Sobolev functions.
Externí odkaz:
http://arxiv.org/abs/2211.01235
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