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Regularity properties of solutions of elliptic equations in R 2 in limit cases

Angela Alberico;  Vincenzo Ferone — 1995

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper the Dirichlet problem for a linear elliptic equation in an open, bounded subset of R 2 is studied. Regularity properties of the solutions are proved, when the data are L 1 -functions or Radon measures. In particular sharp assumptions which guarantee the continuity of solutions are given.

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