General kernel estimates of Schrodinger-type operators with unbounded diffusion terms

被引：0

作者：

Caso, Loredana ^{[1
]}

Kunze, Markus ^{[2
]}

Porfido, Marianna ^{[1
]}

Rhandi, Abdelaziz ^{[1
]}

机构：

[1] Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy

[2] Univ Konstanz, Fachbereich Mahemat & Stat, D-78457 Constance, Germany

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2024年 / 154卷 / 03期

关键词：

Schrodinger-type operator; unbounded coefficients; kernel estimates; ultracontractive semigroup; ELLIPTIC-OPERATORS; COEFFICIENTS; DRIFT;

D O I：

10.1017/prm.2023.45

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We first prove that the realization A(min) of A := div(Q del) - V in L-2(R-d) with unbounded coefficients generates a symmetric sub-Markovian and ultracontractive semigroup on L-2(R-d) which coincides on L-2(R-d) boolean AND C-b(R-d) with the minimal semigroup generated by a realization of A on C-b(R-d). Moreover, using time-dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernel of A and deduce some spectral properties of Amin in the case of polynomially and exponentially growing diffusion and potential coefficients.

引用

页码：929 / 960

页数：32

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