Geodesic
Regularity properties of solutions of elliptic equations in \( \mathbb{R}^{2} \) in limit cases
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 6 (1995) no. 4, pp. 237-250

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper the Dirichlet problem for a linear elliptic equation in an open, bounded subset of \( \mathbb{R}^{2} \) 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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     author = {Alberico, Angela and Ferone, Vincenzo},
     title = {Regularity properties of solutions of elliptic equations in \( {\mathbb{R}^{2}} \) in limit	cases},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {237--250},
     publisher = {mathdoc},
     volume = {Ser. 9, 6},
     number = {4},
     year = {1995},
     zbl = {0860.35015},
     mrnumber = {MR1382708},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1995_9_6_4_a2/}
}
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Alberico, Angela; Ferone, Vincenzo. Regularity properties of solutions of elliptic equations in \( \mathbb{R}^{2} \) in limit	cases. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 6 (1995) no. 4, pp. 237-250. http://geodesic.mathdoc.fr/item/RLIN_1995_9_6_4_a2/