We construct the fundamental solution of second order parabolic equations in non-divergence form under the assumption that the coefficients are of Dini mean oscillation in the spatial variables. We also prove that the fundamental solution satisfies a sub-Gaussian estimate. In the case when the coefficients are Dini continuous in the spatial variables and measurable in the time variable, we establish the Gaussian bounds for the fundamental solutions. We present a method that works equally for second order parabolic systems in non-divergence form.
|Number of pages||35|
|Journal||Journal of Differential Equations|
|Publication status||Published - 2022 Dec 15|
Bibliographical noteFunding Information:
H. Dong was partially supported by the Simons Foundation, grant no. 709545, a Simons fellowship, grant no. 007638, and the NSF under agreement DMS-2055244.S. Kim was partially supported by the National Research Foundation of Korea under agreements NRF-2019R1A2C2002724 and NRF-2022R1A2C1003322.
© 2022 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Applied Mathematics