Differential and Integral Equations

On $C_0$-semigroups generated by elliptic second order differential expressions on $L^p$-spaces

Vitali Liskevich

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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.

Article information

Differential Integral Equations, Volume 9, Number 4 (1996), 811-826.

First available in Project Euclid: 7 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 35J15: Second-order elliptic equations 35K20: Initial-boundary value problems for second-order parabolic equations 47N20: Applications to differential and integral equations


Liskevich, Vitali. On $C_0$-semigroups generated by elliptic second order differential expressions on $L^p$-spaces. Differential Integral Equations 9 (1996), no. 4, 811--826. https://projecteuclid.org/euclid.die/1367969889

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