| Abstract: |
| In this talk, we obtain the interior pointwise $C^{k,\alpha}$ ($k\geq 0$, $ 0 <\alpha< 1 $) regularity for weak solutions of elliptic and parabolic equations in divergence form. The compactness method and perturbation technique are employed. The pointwise regularity is proved in a very simple way and the results are optimal. In addition, these pointwise regularity can be used to characterize the structure of the nodal sets of solutions. |
|