Tuesday, March 7, 2023 - 17:25 in H2
Regularity for local and nonlocal problems with coefficients
A talk in the Nonlocal Equations: Analysis and Numerics 2023 series by
Ho-Sik Lee from Bielefeld
| Abstract: |
In this talk, we consider two topics. The first one is Holder regularity and Harnack's inequality for minimizers of mixed local and nonlocal double phase functionals. To prove these, we investigate a suitable method for combining De Giorgi-Nash-Moser theory of local problems and that of nonlocal problems.
The second one is a nonlocal version of Meyers' example, which gives sharpness of the result of [Kh. Balci, Diening, Giova, Passarelli Di Napoli, SIAM JMA, 2022] in the local case. Considering the fractional Laplace equation with suitable coefficients, we find the relation between the regularity of the solution of the equation and the BMO seminorm of the logarithm of the coefficients.
Within the CRC this talk is associated to the project(s): A7 |
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