Non-divergence evolution operators modeled on Hörmander's vector fields with Dini continuous coefficients

2025/02/26 by Faini, Matteo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.19073

Abstract

In this paper we construct a fundamental solution for operators of the form H = a_ij(x,t) X_i X_j - d/dt (having adopted Einstein's convention on repeated indexes) and we show that the latter satisfies suitable Gaussian estimates. Here the X_i are Hörmander's vector fields generating a Carnot group and A = (a_ij) is a symmetric and uniformly positive-definite matrix with bounded double Dini continuous entries. As a consequence of this procedure we also prove an existence result for the related Cauchy problem, under a Dini-type condition on the source.

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