We consider the Schr\"odinger type operator (1+|x|^\alpha)\Delta+c|x|^{\alpha-2}, for \alpha> 2, c<0 and N>2. Heat kernel estimates of the associated semigroup are obtained using the equivalence between weighted Nash inequalities and ``weighted'' ultracontractivity of a symmetric Markov semigroup. Moreover we give estimates of the eigenfunctions of the operator for large values of |x|.
Kernel estimates for Schrödinger type operators with unbounded coefficients and critical exponents
DURANTE, Tiziana;MANZO, Rosanna;Tacelli, C.
2016-01-01
Abstract
We consider the Schr\"odinger type operator (1+|x|^\alpha)\Delta+c|x|^{\alpha-2}, for \alpha> 2, c<0 and N>2. Heat kernel estimates of the associated semigroup are obtained using the equivalence between weighted Nash inequalities and ``weighted'' ultracontractivity of a symmetric Markov semigroup. Moreover we give estimates of the eigenfunctions of the operator for large values of |x|.File in questo prodotto:
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