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Sharp kernel estimates for elliptic operators with second-order discontinuous coefficients

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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 sharp bounds for the heat kernel and the function.

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Acknowledgements

The authors thank Prof. M. Choulli for several discussions on the topic and for pointing out reference [3].

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Authors and Affiliations

  1. Dipartimento di Matematica “Ennio De Giorgi”, Università Del Salento, C.P. 193, 73100, Lecce, Italy

    G. Metafune, L. Negro & C. Spina

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  1. G. Metafune
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  2. L. Negro
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  3. C. Spina
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Correspondence to C. Spina.

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Metafune, G., Negro, L. & Spina, C. Sharp kernel estimates for elliptic operators with second-order discontinuous coefficients. J. Evol. Equ. 18, 467–514 (2018). https://doi.org/10.1007/s00028-017-0408-0

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  • DOI: https://doi.org/10.1007/s00028-017-0408-0

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