We consider the Schrödinger type operator A=(1+|x|^a)-|x|^b, for a in [0,2] and bge 0. We prove that, for any p in (1,+oo), the minimal realization of operator A in L^p(R^N) generates a strongly continuous analytic semigroup (T_p(t))_{tge 0}. For a in [0,2) and β≥2, we then prove some upper estimates for the heat kernel k associated with the semigroup (T_p(t))_{tge 0}. As a consequence, we obtain an estimate for large |x| of the eigenfunctions of A. Finally, we extend such estimates to a class of divergence type elliptic operators

On Schr"odinger type operators with unbounded coefficients: generation and heat kernel estimates / Lorenzi, Luca Francesco Giuseppe; A., Rhandi. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 15:1(2015), pp. 53-88. [10.1007/s00028-014-0249-z]

On Schr"odinger type operators with unbounded coefficients: generation and heat kernel estimates

LORENZI, Luca Francesco Giuseppe
;
2015

Abstract

We consider the Schrödinger type operator A=(1+|x|^a)-|x|^b, for a in [0,2] and bge 0. We prove that, for any p in (1,+oo), the minimal realization of operator A in L^p(R^N) generates a strongly continuous analytic semigroup (T_p(t))_{tge 0}. For a in [0,2) and β≥2, we then prove some upper estimates for the heat kernel k associated with the semigroup (T_p(t))_{tge 0}. As a consequence, we obtain an estimate for large |x| of the eigenfunctions of A. Finally, we extend such estimates to a class of divergence type elliptic operators
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2762749
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 21
  • ???jsp.display-item.citation.isi??? 21
social impact