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Kernel estimates for elliptic operators with second-order discontinuous coefficients

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Abstract

We study parabolic problems associated to the second-order elliptic operator

$$L = \Delta + (a-1)\sum_{i,j=1}^N\frac{x_{i}x_{j}}{|x|^2}D_{ij}+c\frac{x}{|x|^2}\cdot\nabla - b|x|^{-2}$$

with a > 0 and b, c real coefficients and prove kernel estimates for the transition kernel.

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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, M. Sobajima & C. Spina

  2. Department of Mathematics, Tokyo University of Science, Tokyo, Japan

    M. Sobajima

Authors
  1. G. Metafune
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  2. M. Sobajima
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  3. C. Spina
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Correspondence to G. Metafune.

Additional information

Dedicated to Jan Prüss on the occasion of his 65th anniversary.

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Metafune, G., Sobajima, M. & Spina, C. Kernel estimates for elliptic operators with second-order discontinuous coefficients. J. Evol. Equ. 17, 485–522 (2017). https://doi.org/10.1007/s00028-016-0355-1

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  • DOI: https://doi.org/10.1007/s00028-016-0355-1

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