Volume 23, Number 3, July-September 2017
|Page(s)||937 - 976|
|Published online||03 May 2017|
On coupled systems of Kolmogorov equations with applications to stochastic differential games∗
1 Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via Cozzi 55, 20125 Milano, Italy.
2 Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Via per Arnesano, 73100 Lecce, Italy.
3 Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy.
Received: 16 June 2015
Accepted: 13 April 2016
We prove that a family of linear bounded evolution operators (G(t,s))t ≥ s ∈ I can be associated, in the space of vector-valued bounded and continuous functions, to a class of systems of elliptic operators 𝒜 with unbounded coefficients defined in I × ℝd (where I is a right-halfline or I =ℝ) all having the same principal part. We establish some continuity and representation properties of (G(t,s))t ≥ s ∈ I and a sufficient condition for the evolution operator to be compact in Cb(ℝd;ℝm). We prove also a uniform weighted gradient estimate and some of its more relevant consequence.
Mathematics Subject Classification: 35K45 / 35K58 / 47B07 / 60H10 / 91A15
Key words: Nonautonomous parabolic systems / unbounded coefficients / evolution operators / compactness / gradient estimates / semilinear systems / stochastic games
© EDP Sciences, SMAI 2017
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