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

2010/08/03 by Angiuli, Luciana, Lorenzi, Luca
#35K10 #35K15 #47B07 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1008.0560

Abstract

In this paper we consider nonautonomous elliptic operators \mathcal A with nontrivial potential term defined in I×\mathbb R^d, where I is a right-halfline (possibly I=\mathbb R). We prove that we can associate an evolution operator (G(t,s)) with \mathcal A in the space of all bounded and continuous functions on \mathbb 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 C₀(\mathbb R^d).

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