Viscosity solutions of the Monge–Ampère equation with the right hand side in
Anna Lisa Amadori
Università degli Studi di Napoli 'Parthenope', ItalyBarbara Brandolini
Università degli Studi di Napoli Federico II, ItalyCristina Trombetti
Università degli Studi di Napoli Federico II, Italy
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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 -viscosity solutions.
Cite this article
Anna Lisa Amadori, Barbara Brandolini, Cristina Trombetti, Viscosity solutions of the Monge–Ampère equation with the right hand side in . Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 3, pp. 221–233
DOI 10.4171/RLM/491