JournalsrlmVol. 30, No. 4pp. 701–732

The Dirichlet problem with VMO data in upper-graph Lipschitz domains

  • Dorina Mitrea

    Baylor University, Waco, USA
  • Irina Mitrea

    Temple University, Philadelphia, USA
  • Marius Mitrea

    Baylor University, Waco, USA
The Dirichlet problem with VMO data in upper-graph Lipschitz domains cover
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Abstract

In this paper we take up the study of the Dirichlet problem for elliptic operators in upper-graph Lipschitz domains, with boundary values (taken in a pointwise nontangential sense) belonging to the Sarason space of functions with vanishing mean oscillations. We employ certain modified versions of boundary layer potentials in order to construct solutions satisfying certain vanishing Carleson measure conditions.

Cite this article

Dorina Mitrea, Irina Mitrea, Marius Mitrea, The Dirichlet problem with VMO data in upper-graph Lipschitz domains. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 4, pp. 701–732

DOI 10.4171/RLM/868