sobolev mappings
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2021 ◽  
Vol 14 (6) ◽  
pp. 1851-1871
Author(s):  
Petru Mironescu ◽  
Jean Van Schaftingen

2021 ◽  
Vol 30 (2) ◽  
pp. 281-299
Author(s):  
Petru Mironescu ◽  
Jean Van Schaftingen

2020 ◽  
Vol 249 (5) ◽  
pp. 754-768
Author(s):  
Evgenii A. Sevost’yanov ◽  
Alexander Ukhlov

2020 ◽  
Vol 17 (2) ◽  
pp. 215-233
Author(s):  
Evgenii Sevost'yanov ◽  
Alexander Ukhlov

We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities ($Q$-homeomor\-phisms) with a locally integrable function $Q$ are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem, we prove that, on the Carnot groups $\mathbb G,$ the mappings inverse to Sobolev homeomorphisms of finite distortion of the class $W^1_{\nu,\loc}(\Omega;\Omega')$ belong to the Sobolev class $W^1_{1,\loc}(\Omega';\Omega)$.


2020 ◽  
Vol 2020 (763) ◽  
pp. 79-109
Author(s):  
Alexander Lytchak ◽  
Stefan Wenger ◽  
Robert Young

AbstractThe Dehn function measures the area of minimal discs that fill closed curves in a space; it is an important invariant in analysis, geometry, and geometric group theory. There are several equivalent ways to define the Dehn function, varying according to the type of disc used. In this paper, we introduce a new definition of the Dehn function and use it to prove several theorems. First, we generalize the quasi-isometry invariance of the Dehn function to a broad class of spaces. Second, we prove Hölder extension properties for spaces with quadratic Dehn function and their asymptotic cones. Finally, we show that ultralimits and asymptotic cones of spaces with quadratic Dehn function also have quadratic Dehn function. The proofs of our results rely on recent existence and regularity results for area-minimizing Sobolev mappings in metric spaces.


2020 ◽  
Vol 148 (7) ◽  
pp. 2877-2891 ◽  
Author(s):  
Armin Schikorra ◽  
Jean Van Schaftingen
Keyword(s):  

2019 ◽  
Vol 60 (5) ◽  
pp. 916-926 ◽  
Author(s):  
A. Ferone ◽  
M. V. Korobkov ◽  
A. Roviello

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