The abstract Lewy-Stampacchia inequality and applications
By Nicola Gigli, Sunra Mosconi. 2014
49 citations recorded by the source corpus.
We prove an abstract and general version of the Lewy-Stampacchia inequality. We then show how to reproduce more classical versions of it and, more importantly, how it can be used in conjunction with Laplacian comparison estimates to produce large class of functions with bounded Laplacian on spaces with a lower bound on the Ricci curvature.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2c0c65f2ffc032f9a3173726294cc933bbb646c1
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
In Mathematical Physics
Citations in the corpus
- Non-collapsed spaces with Ricci curvature bounded from below (2017, unknown): “…i.e. Lipschitz and with bounded Laplacian - in the context of Ricci-limit spaces has been proved in [16] and frequently used as important technical tool in [17, 18, 19, 20, 21, 22]; their existence in the RCD setting has been proved in [8, Lemma 6.7] and [35, Theorem 3.12], see also [45, Lemma 3.1]”
- Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows (2018, background): “2 below, we will see how the Lewy-Stampacchia inequality, proved in this abstract framework by Gigli-Mosconi in [43], allows us to give an (almost) affirmative answer to this question.”