The co-area formula for Sobolev mappings
By Jan Maly, David Swanson, William P. Ziemer. 2001
138 citations recorded by the source corpus.
We extend Federer's co-area formula to mappings f belonging to the Sobolev class W 1,p (R n ;R m ), 1 ≤ m m, and more generally, to mappings with gradient in the Lorentz space L m,1 (R n ). This is accomplished by showing that the graph of f in R n+m is a Hausdorff n-rectifiable set.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/873ca6d074f56c97d96b333cbb99214c9e48d7ab
How researchers see this paper
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In Applied Mathematics
- Juha Kinnunen
- P. Hajłasz
- R. Korte
- Heli Tuominen
- Nageswari Shanmugalingam
- Giandomenico Orlandi
- Sisto Baldo
- Giovanni S. Alberti
In Geometry and Topology
- P. Hajłasz
- Heli Tuominen
- Nageswari Shanmugalingam
- R. Korte
- Juha Kinnunen
- Pawel Strzelecki
- Alessio Figalli
- Giandomenico Orlandi
Citations in the corpus
- Functions with prescribed singularities (2003, result): “It has been recently proved in [ 30 ] that the same is true when u is the precise representative of a map of class W1,p for some p > h.”
- Lebesgue points and capacities via the boxing inequality in metric spaces (2008, methodology): “In the Euclidean setting this has been obtained in [Fl], see also [Ma2] and [ MSZ ].”
- A simple proof of the Morse-Sard theorem in Sobolev spaces (2008, background): “We remark that, in the case n = m, the result is just a corollary of the area formula for Sobolev functions 1 (for a proof and for more references on the subject, see [5]), so we can assume n > m, that is, k ≥ 2.”
- Sard's theorem for mappings in Hölder and Sobolev spaces (2005, background): “) For other results related to the Sard theorem for Sobolev mappings see [14] and [17].”
- Transport Equations for Semiconductors (2009, unknown): “, [30, 46]).”