Differentiability in the Sobolev space W1,n-1
Tengvall, V. (2014). Differentiability in the Sobolev space W1,n-1. Calculus of variations and partial differential equations, 51(1-2), 381-399. https://doi.org/10.1007/s00526-013-0679-4
Julkaistu sarjassa
Calculus of variations and partial differential equationsTekijät
Päivämäärä
2014Tekijänoikeudet
© Springer-Verlag Berlin Heidelberg 2013. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
Let Ω ⊂ Rn be a domain, n ≥ 2. We show that a continuous, open and
discrete mapping f ∈ W1,n−1
loc (Ω, Rn
) with integrable inner distortion is differentiable
almost everywhere on Ω. As a corollary we get that the branch set of such a mapping
has measure zero.
Julkaisija
SpringerISSN Hae Julkaisufoorumista
0944-2669Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/23809293
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Sharpness of the differentiability almost everywhere and capacitary estimates for Sobolev mappings
Hencl, Stanislav; Tengvall, Ville (European Mathematical Society Publishing House; Real Sociedad Matematica Espanola, 2017)We give sharp conformal conditions for the dfferentiability in the Sobolev space W1, n-1 loc (Ω,Rn). Furthermore, we show that the space W1, n-1 loc (Ω,Rn) can be considered as the borderline space for some capacitary ... -
Function spaces and pseudo-differential operators on vector bundles
Uusluoto, Veli-Pekka (2019)The objective of this Master thesis is to give coordinate-free definitions of certain concepts in modern analysis on vector bundles and to apply these tools to elliptic partial differential equations. Topics that we cover ... -
Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential
Eriksson-Bique, Sylvester; Soultanis, Elefterios (Mathematical Sciences Publishers, 2024)We represent minimal upper gradients of Newtonian functions, in the range 1≤p<∞, by maximal directional derivatives along “generic” curves passing through a given point, using plan-modulus duality and disintegration ... -
Differential structure associated to axiomatic Sobolev spaces
Giglia, Nicola; Pasqualetto, Enrico (Elsevier GmbH, Urban und Fischer, 2020)The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure. -
Differential of metric valued Sobolev maps
Gigli, Nicola; Pasqualetto, Enrico; Soultanis, Elefterios (Elsevier, 2020)We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.