In this paper we give sufficient conditions on $\alpha \ge 0$ and $c\in \R$ ensuring that the space of test functions $C_c^\infty(\R^N)$ is a core for the operator $$L_0u=(1+|x|^\alpha )\Delta u+\frac{c}{|x|^2}u=:Lu+\frac{c}{|x|^2}u,$$ and $L_0$ with a suitable domain generates a quasi-contractive and positivity preserving $C_0$-semigroup in $L^p(\R^N),\,1<p<\infty$. The proofs are based on some $L^p$-weighted Hardy's inequality and perturbation techniques.
Elliptic operators with unbounded diffusion coefficients perturbed by inverse square potentials in Lp-spaces
RHANDI, Abdelaziz;GREGORIO, FEDERICA
2016-01-01
Abstract
In this paper we give sufficient conditions on $\alpha \ge 0$ and $c\in \R$ ensuring that the space of test functions $C_c^\infty(\R^N)$ is a core for the operator $$L_0u=(1+|x|^\alpha )\Delta u+\frac{c}{|x|^2}u=:Lu+\frac{c}{|x|^2}u,$$ and $L_0$ with a suitable domain generates a quasi-contractive and positivity preserving $C_0$-semigroup in $L^p(\R^N),\,1File in questo prodotto:
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