Non-divergence evolution operators modeled on Hörmander vector fields with Dini continuous coefficients
Abstract
In this paper we analyze operators $ H = \partial_t-\sum_{i, j} a_{ij}(x, t) X_i X_j $, where the $ X_i $'s are Hörmander vector fields generating a Carnot group and $ A = [a_{ij}] $ is a symmetric and uniformly positive-definite matrix whose entries satisfy double Dini continuity, a strictly weaker condition than Hölder continuity. For these operators, we build a fundamental solution and show a two-sided Gaussian estimate for the latter, as well as upper Gaussian estimates for its derivatives up to weight $ 2 $. As a consequence, we prove an existence result for the related Cauchy problem, under a Dini-type condition on the source.
Fields of Study & Subjects
Holomorphic and Operator Theory
Approximation Theory and Sequence Spaces
advanced mathematical theories
Publication details
- Journal / source
- Mathematics in Engineering
- Volume
- 8
- Issue
- 4
- Pages
- 477–518
- Publication date
- 1 January 2026
- Language
- EN