Compactness and invariance properties of evolution operators associated with Kolmogorov operators with unbounded coefficients

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:379

Article

Angiuli, Luciana²  Lorenzi, Luca¹ 

[1] Univ Parma, Dipartimento Matemat, I-43124 Parma, Italy

[2] Univ Salento, Dipartimento Matemat Ennio De Giorgi, I-73100 Lecce, Italy

关键词: Nonautonomous second-order elliptic operators;    Unbounded coefficients;    Evolution operators;    Compactness;    Invariant subspaces;   

DOI  :  10.1016/j.jmaa.2010.12.029

来源: Elsevier

【 摘 要 】

In this paper we consider nonautonomous elliptic operators A with nontrivial potential term defined in I x R-d. where I is a right-halfline (possibly I = R). We prove that we can associate an evolution operator (G (t, s)) with A in the space of all bounded and continuous functions on R-d. We also study the compactness properties of the operator G(t, s). Finally. we provide sufficient conditions guaranteeing that each operator G(t, s) preserves the usual L-p-spaces and C-0(R-d). (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free