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1996 On $C_0$-semigroups generated by elliptic second order differential expressions on $L^p$-spaces
Vitali Liskevich
Differential Integral Equations 9(4): 811-826 (1996).

Abstract

We study well-posedness in $L^P$ of the Cauchy problem for second order parabolic equations with time-independent measurable coefficients by means of constructing corresponding Cosernigroups. Lower order terms are considered as form-bounded perturbations of the generator of the symmetric submarkovian sernigroup associated with the Dirichlet form. It is shown that the Cosernigroup corresponding to the Cauchy problem exists in a certain interval in the scale of $L^P$-spaces which depends only on form-bounds of perturbations. We establish also analyticity and $L^P$ -smoothness of the sernigroup constructed.

Citation

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Vitali Liskevich. "On $C_0$-semigroups generated by elliptic second order differential expressions on $L^p$-spaces." Differential Integral Equations 9 (4) 811 - 826, 1996.

Information

Published: 1996
First available in Project Euclid: 7 May 2013

zbMATH: 0852.47018
MathSciNet: MR1401439

Subjects:
Primary: 47D06
Secondary: 35J15 , 35K20 , 47N20

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.9 • No. 4 • 1996
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