We compare various notions of solutions of Monge-Ampère equations with discontinuous functions on 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.
Amadori A.L., Brandolini B., Trombetti C. (2007). Viscosity solutions of the Monge-Ampère equation with the right hand side in Lp. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 18(3), 221-233.
Viscosity solutions of the Monge-Ampère equation with the right hand side in Lp
Brandolini B.;
2007-01-01
Abstract
We compare various notions of solutions of Monge-Ampère equations with discontinuous functions on 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.
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