| Abstract: |
| We analyze recent novel regularity theory for fractional power of parabolic operators in divergence form. These equations are fundamental in continuous time random walk models and appear as generalized Master equation. These equations are non-local in nature and were studied by Luis Caffarelli and Luis Silvestre. We developed a parabolic method of semigroups that allows us to prove a local extension problem. As a consequence we obtain interior and global parabolic Schauder estimates. For that, we also prove a characterization of the correct intermediate parabolic H\older spaces in the spirit of Sergio Campanato. This work is jointly done with Marta de Le\`on-Contreras (Universidad of Reading, UK) and Pablo Ra\`ul Stinga (Iowa State University). |
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