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May/June 2014 Elliptic operators with unbounded diffusion and drift coefficients in $L^p$ spaces
G. Metafune, C. Spina, C. Tacelli
Adv. Differential Equations 19(5/6): 473-526 (May/June 2014).

Abstract

We prove that, for $\alpha > 2$, $\frac{N}{N-2+c} < p <\infty$, the operator $Lu=(1+|x|^\alpha)\Delta u+c|x|^{\alpha-1}\tfrac{x}{|x|}\cdot\nabla$ generates an analytic semigroup in $L^p$, which is contractive if and only if $p \ge \frac{N+\alpha-2}{N-2+c}$. Moreover, for $\alpha <\frac{N}{p'}+c$, we provide an explicit description of the domain. Spectral properties of the operator $L$ and kernel estimates are also obtained.

Citation

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G. Metafune. C. Spina. C. Tacelli. "Elliptic operators with unbounded diffusion and drift coefficients in $L^p$ spaces." Adv. Differential Equations 19 (5/6) 473 - 526, May/June 2014.

Information

Published: May/June 2014
First available in Project Euclid: 3 April 2014

zbMATH: 1305.47029
MathSciNet: MR3189092

Subjects:
Primary: 35B50 , 35J25 , 35J70 , 47D07

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.19 • No. 5/6 • May/June 2014
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