JournalsrlmVol. 18, No. 3pp. 221–233

Viscosity solutions of the Monge–Ampère equation with the right hand side in <em>L<sup>p</sup></em>

  • Cristina Trombetti

    Università degli Studi di Napoli Federico II, Italy
  • Barbara Brandolini

    Università degli Studi di Napoli Federico II, Italy
  • Anna Lisa Amadori

    Università degli Studi di Napoli 'Parthenope', Italy
Viscosity solutions of the Monge–Ampère equation with the right hand side in <em>L<sup>p</sup></em> cover
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Abstract

In this paper we compare various notions of solutions of Monge–Ampère equations with discontinuous functions in the right hand side. Precisely, we show that the weak solutions defined by Trudinger can be obtained by the vanishing viscosity approximation method. Moreover, we investigate existence and uniqueness of Lp-viscosity solutions.

Cite this article

Cristina Trombetti, Barbara Brandolini, Anna Lisa Amadori, Viscosity solutions of the Monge–Ampère equation with the right hand side in <em>L<sup>p</sup></em>. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 3, pp. 221–233

DOI 10.4171/RLM/491