Geodesic
On coupled systems of Kolmogorov equations with applications to stochastic differential games
Addona, Davide1 ; Angiuli, Luciana2 ; Lorenzi, Luca3 ; Tessitore, Gianmario1 
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.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 937-976

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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 × ℝ d (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 C b ( ℝ d ; ℝ m ) . We prove also a uniform weighted gradient estimate and some of its more relevant consequence.

DOI : 10.1051/cocv/2016019
Classification : 35K45, 35K58, 47B07, 60H10, 91A15
Keywords: Nonautonomous parabolic systems, unbounded coefficients, evolution operators, compactness, gradient estimates, semilinear systems, stochastic games

Addona, Davide 1 ; Angiuli, Luciana 2 ; Lorenzi, Luca 3 ; Tessitore, Gianmario 1

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. 
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     title = {On coupled systems of {Kolmogorov} equations with applications to stochastic differential games},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {937--976},
     publisher = {EDP-Sciences},
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Addona, Davide; Angiuli, Luciana; Lorenzi, Luca; Tessitore, Gianmario. On coupled systems of Kolmogorov equations with applications to stochastic differential games. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 937-976. doi: 10.1051/cocv/2016019

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