The fractional powers of the sub-Laplacian in Carnot groups through an analytic continuation

2023/10/26 by Francesca Corni, Corni, Francesca, Fausto Ferrari +1 · 1 citation
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2310.17387

Abstract

In this paper we construct the fractional powers of the sub-Laplacian in Carnot groups through an analytic continuation approach. In addition, we characterize the powers of the fractional sub-Laplacian in the Heisenberg group, and as a byproduct we compute the k-th order momenta with respect to the heat kernel.

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• Fujita exponent for the fractional sub-Laplace semilinear heat equation with forcing term on the Heisenberg group

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