Riesz transform under perturbations via heat kernel regularity. (English. French summary) Zbl 1433.58023
The main purpose of this paper is to study the behavior of the Riesz transform under metric perturbations in the abstract setting of complete, connected and non-compact \(n\)-dimensional Riemannian manifolds. As a byproduct, the authors also establish stability and instability of gradient estimates of harmonic functions and heat
kernels under metric perturbation. Other related results in this paper include the case of degenerate elliptic equations on the whole space and remarks on the conic Laplace operators.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
MSC:
| 58J37 | Perturbations of PDEs on manifolds; asymptotics |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 58J05 | Elliptic equations on manifolds, general theory |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35K05 | Heat equation |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
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