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- W2949816734 abstract "We consider the Schrodinger type operator ${mathcal A}=(1+|x|^{alpha})Delta-|x|^{beta}$, for $alphain [0,2]$ and $betage 0$. We prove that, for any $pin (1,infty)$, the minimal realization of operator ${mathcal A}$ in $L^p(R^N)$ generates a strongly continuous analytic semigroup $(T_p(t))_{tge 0}$. For $alphain [0,2)$ and $betage 2$, we then prove some upper estimates for the heat kernel $k$ associated to the semigroup $(T_p(t))_{tge 0}$. As a consequence we obtain an estimate for large $|x|$ of the eigenfunctions of ${mathcal A}$. Finally, we extend such estimates to a class of divergence type elliptic operators." @default.
- W2949816734 created "2019-06-27" @default.
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- W2949816734 date "2012-03-04" @default.
- W2949816734 modified "2023-09-27" @default.
- W2949816734 title "On Schroedinger type operators with unbounded coefficients: Generation and heat kernel estimates" @default.
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