Title: The Dirichlet problem for elliptic operators on rough domains
Speaker: Mingming Cao（CSIC, ICMAT）
Time: November 17, 2022. 16:00-17:00
Location: Tencent meeting , Meeting ID:468 902 773, Password:123456
Abstract：In capacity density open sets, we give a geometric characterization of well-posedness of the Dirichlet problem for elliptic operators with boundary data in Holder spaces. By means of a weak connectivity assumption, we establish the well-posedness of the Dirichlet problem when the solution satisfies a Carleson measure estimate and the boundary data belongs to Holder or Morrey-Campanato spaces. We also present a characterization of the Holder spaces in terms of the boundary traces of solutions. Finally, in 1-sided chord-arc domains, we establish an equivalence between Holder and Carleson norms.
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