On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem |
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Authors: | R Mikulevičius H Pragarauskas |
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Institution: | 1. University of Southern California, Los Angeles, United States;2. Institute of Mathematics and Informatics, University of Vilnius, Vilnius, Lithuania |
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Abstract: | The existence and uniqueness in Sobolev spaces of solutions of the Cauchy problem to parabolic integro-differential equation with variable coefficients 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. |
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Keywords: | 45K05 60J75 35B65 |
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