High order Fefferman-Phong type inequalities in Carnot groups and regularity for degenerate elliptic operators plus a potential
type: Item
instance of: scholarly article
title: High order Fefferman-Phong type inequalities in Carnot groups and regularity for degenerate elliptic operators plus a potential
zbMATH Open document ID: 1470.35377
DOI: 10.1155/2014/274859
author: Kelei Zhang
author: Pengcheng Niu
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Let \(\{X_1, X_2, \dots, X_m \}\) be the basis of space of horizontal vector fields in a Carnot group \(\mathbb{G} = (\mathbb{R}^n; \circ)\) \( (m < n)\). We prove high order Fefferman-Phong type inequalities in \(\mathbb{G}\). As applications, we derive a priori \(L^p(\mathbb{G})\) estimates for the nondivergence degenerate elliptic operators \(L = - \sum_{i, j = 1}^m a_{i j}(x) X_i X_j + V(x)\) with \(V M O\) coefficients and a potential \(V\) belonging to an appropriate Stummel type class introduced in this paper. Some of our results are also new even for the usual Euclidean space.
Mathematics Subject Classification ID: 35R03
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 7022067
Wikidata QID: Q59037441
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/274859
OpenAlex ID: W2147906201
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description: scientific article; zbMATH DE number 7022067