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 $L^p$-viscosity solutions.
Viscosity solutions of the Monge-Ampère equation with the right hand side in $Lsp p$ / A. L., Amadori; Brandolini, Barbara; Trombetti, Cristina. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - STAMPA. - 18:(2007), pp. 221-233.
Viscosity solutions of the Monge-Ampère equation with the right hand side in $Lsp p$
BRANDOLINI, BARBARA;TROMBETTI, CRISTINA
2007
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 $L^p$-viscosity solutions.File in questo prodotto:
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