Boundary higher integrability for very weak solutions of quasilinear parabolic equations
Dr. Karthik Adimurthi, Seoul National University
| Speaker |
Dr. Karthik Adimurthi, Seoul National University
|
|---|---|
| When |
Jun 23, 2017
from 11:00 AM to 12:00 PM |
| Where | LH 006 |
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Abstract: We prove boundary integrability for the (spatial) gradient of very weak solutions of quasilinear parabolic equations modeled on the p-laplacian operator. To this end, we prove that the gradients
satisfy a reverse H\"older inequality near the boundary. In order to do this, we construct a suitable test function which is Lipschitz continuous and preserves the boundary values. These results are new even for
linear parabolic equations on domains with smooth boundary and are also applicable for systems as well as higher order parabolic equations. This is joint work with Sun-Sig Byun.