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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.