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pro vyhledávání: '"primary 26b30"'
Within the context of rough path analysis via fractional calculus, we show how the notion of variability can be used to prove the existence of integrals with respect to H\"older continuous multiplicative functionals in the case of Lipschitz coefficie
Externí odkaz:
http://arxiv.org/abs/2407.06907
We analyze some properties of the measures in the dual of the space $BV$, by considering (signed) Radon measures satisfying a perimeter bound condition, which means that the absolute value of the measure of a set is controlled by the perimeter of the
Externí odkaz:
http://arxiv.org/abs/2407.06224
Autor:
Comi, Giovanni E., Stefani, Giorgio
We continue the study of the fine properties of sets having locally finite distributional fractional perimeter. We refine the characterization of their blow-ups and prove a Leibniz rule for the intersection of sets with locally finite distributional
Externí odkaz:
http://arxiv.org/abs/2303.10989
Publikováno v:
Electron. J. Probab. 27 (2022), no. 73, 1--29
We prove a result on the fractional Sobolev regularity of composition of paths of low fractional Sobolev regularity with functions of bounded variation. The result relies on the notion of variability, proposed by us in the previous article [43, arXiv
Externí odkaz:
http://arxiv.org/abs/2105.06249
Autor:
Brudnyi, A., Brudnyi, Yu.
We introduce and study spaces of multivariate functions of bounded variation generalizing the classical Jordan and Wiener spaces. Multivariate generalizations of the Jordan space were given by several prominent researchers but each of them preserved
Externí odkaz:
http://arxiv.org/abs/1811.07233
Autor:
Brudnyi, Alexander, Brudnyi, Yuri
We introduce and study multivariate generalizations of the classical BV spaces of Jordan, F. Riesz and Wiener. The family of the introduced spaces contains or is intimately related to a considerable class of function spaces of modern analysis includi
Externí odkaz:
http://arxiv.org/abs/1806.08824
Autor:
Malý, Lukáš
Trace classes of Sobolev-type functions in metric spaces are subject of this paper. In particular, functions on domains whose boundary has an upper codimension-$\theta$ bound are considered. Based on a Poincar\'e inequality, existence of a Borel meas
Externí odkaz:
http://arxiv.org/abs/1704.06344
In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develo
Externí odkaz:
http://arxiv.org/abs/1410.2228
Autor:
Randrianantoanina, Beata, Xu, Huaqiang
We show that the classes of $\alpha$-absolutely continuous functions in the sense of Bongiorno coincide for all $0<\alpha<1$.
Comment: 6 pages, 1 figure; this paper is a partial replacement of the withdrawn paper Arxiv 1306.4291
Comment: 6 pages, 1 figure; this paper is a partial replacement of the withdrawn paper Arxiv 1306.4291
Externí odkaz:
http://arxiv.org/abs/1404.0064
Autor:
Capriani, Giuseppe Maria
We analyze the Steiner rearrangement in any codimension of Sobolev and $BV$ functions. In particular, we prove a P\'olya-Szeg\H{o} inequality for a large class of convex integrals. Then, we give minimal assumptions under which functions attaining equ
Externí odkaz:
http://arxiv.org/abs/1112.3845