| Abstract: |
| We will build up some of the tools required to prove local boundedness and Harnack inequalities for equations driven by fractional powers of nondivergence form elliptic operators.The first main difficulty we will discuss is how to define fractional powers of nondivergence form operators since, in principle, there is no natural Hilbert space structure. In order to overcome the nonlocality of these fractional operator, we will use the extension problem introduced by Caffarelli--Silvestre for the fractional Laplacian to study the desired regularity estimates of a degenerate but local PDE. This ongoing work is joint with my advisor Pablo Ra\`ul Stinga (Iowa State University). |
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