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Gradient Estimates for Elliptic Operators with Second-Order Discontinuous Coefficients

  • G. MetafuneEmail author
  • L. Negro
  • C. Spina
Article
  • 40 Downloads

Abstract

We consider the second-order elliptic operator
$$\begin{aligned} L =\Delta +(a-1)\sum _{i,j=1}^N\frac{x_ix_j}{|x|^2}D_{ij}+c\frac{x}{|x|^2}\cdot \nabla -\frac{b}{|x|^{2}}, \end{aligned}$$
\(a>0\), \(b,\ c \in \mathbb {R}\) and we prove gradient estimates for the heat kernel.

Keywords

Elliptic operators discontinuous coefficients analytic semigroups kernel estimates 

Mathematics Subject Classification

47D07 35B50 35J25 35J70 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica “Ennio De Giorgi”Università del SalentoLecceItaly

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