## Differential and Integral Equations

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

Vitali Liskevich

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 7 May 2013

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