No abstract

The existence and uniqueness in Hölder spaces of solutions of the Cauchy problem to parabolic integro-differential equation of the order α ∈ (0, 2) is investigated. The principal part of the operator has kernel m(t, x, y)/|y| d+α with a bounded nondegenerate m, Hölder in x and measurable in y. The result is applied to prove the uniqueness of the corresponding martingale problem.MSC classes: 45K05, 60J75, 35B65

The existence and uniqueness in Sobolev spaces of solutions of the Cauchy problem to parabolic integro-differential equation of the order α ∈ (0, 2) is investigated. The principal part of the operator has kernel m(t, x, y)/|y| d+α with a bounded nondegenerate m, Hölder in x and measurable in y. The lower order part has bounded and measurable coefficients. The result is applied to prove the existence and uniqueness of the corresponding martingale problem.MSC classes: 45K05, 60J75, 35B65

No abstract