Independence on p of weak upper gradients on RCD spaces
By Nicola Gigli, B. Han. 2014
64 citations recorded by the source corpus.
We study p-weak gradients on RCD(K,∞) metric measure spaces and prove that they all coincide for p>1. On proper spaces, our arguments also cover the extremal situation of BV functions.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/4ed33b449685cfc9a353f2877219cc8b4dc25acf
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Nicola Gigli
- Luigi Ambrosio
- Elia Brué
- Enrico Pasqualetto
- Daniele Semola
- Semola Daniele
- Simone Di Marino
- Giuseppe Savar'e
In Geometry and Topology
- Nicola Gigli
- Luigi Ambrosio
- Elia Brué
- Semola Daniele
- Simone Di Marino
- Enrico Pasqualetto
- Daniele Semola
- Fabrice Baudoin
Citations in the corpus
- Perimeter as relaxed Minkowski content in metric measure spaces (2016, methodology): “On the other hand, in [GiHa] it has been proved that on RCD(K,∞) spaces the p-weak gradients all coincide even for p = 1 (this result is based on the Bakry-Emery estimate in the form established by Savaré in [Sa]), thus giving the claim.”
- Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces. (2019, background): “Furthermore in [30] it has been proved that on any proper RCD(K,∞) m.”
- Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, methodology): “asi Bakry-Emery curvature condition (´ 8) is indeed weaker than BE(0,∞). In the context of RCD spaces, the relation between the conditions RCD(0,∞) and BE(0,∞) is discussed in detail in [5], [10] and [37]. 3 BV class and co-area formula In this section we use the Dirichlet form and the associated fa”
- Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows (2018, background): “One of the main contributions of [41] has been to prove, roughly speaking, that, under the RCD.”