We prove that a family of linear bounded evolution operators (G(t, s))t=sI 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=sI 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.
Addona, D., Angiuli, L., Lorenzi, L., Tessitore, G. (2017). On coupled systems of Kolmogorov equations with applications to stochastic differential games. ESAIM. COCV, 23(3), 937-976 [10.1051/cocv/2016019].
On coupled systems of Kolmogorov equations with applications to stochastic differential games
Addona, Davide;Tessitore, Gianmario
2017
Abstract
We prove that a family of linear bounded evolution operators (G(t, s))t=sI 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=sI 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.
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