On the Cauchy Problem for Integro-differential Operators in Hölder Classes and the Uniqueness of the Martingale Problem
By R. Mikulevičius, H. Pragarauskas. 2011
82 citations recorded by the source corpus.
The existence and uniqueness in Hölder spaces of classical 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/c20b656f133036ecb27a229c2c203cb16d5e3ffc
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In Applied Mathematics
- Luis Silvestre
- C. Imbert
- H. Pragarauskas
- R. Mikulevičius
- Russell W. Schwab
- Juan Luis V'azquez
- Enrico Valdinoci
- Xavier Ros-Oton
In Computational Theory and Mathematics
- Luis Silvestre
- C. Imbert
- H. Pragarauskas
- R. Mikulevičius
- Enrico Valdinoci
- Russell W. Schwab
- Xavier Ros-Oton
- Luis Caffarelli
Citations in the corpus
- On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem (2011, result): “Since the lower part of L has only measurable coefficients, we generalize the results in [13].”
- The Schauder estimate for kinetic integral equations (2018, background): “Schauder estimates for integro-differential equations have been obtained in recent years, see [14, 11, 19, 20, 8, 3].”