Wednesday, February 16, 2022 - 15:15 in ZOOM - Video Conference
On the Kolmogorov equations with coefficients of low regularity
A talk in the Bielefeld Stochastic Afternoon series by
Stanislav Shaposhnikov
| Abstract: |
We consider the stationary Kolmogorov equation in the case where the
positive definite diffusion matrix is continuous and the drift
coefficient is locally integrable to a power greater than the
dimension. Note that even in the one-dimensional case a solution can
fail to have the Sobolev derivative. Moreover there is an example of
a positive definite and continuous diffusion matrix for which the
equation has a locally unbounded solution. We present several new
results: the Harnack inequality, sufficient conditions for the local
exponential integrability, the Sobolev regularity of the ratio of
two nonnegative solutions.
We also present new existence and uniqueness results.
Within the CRC this talk is associated to the project(s): A5 |
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