Viscosity solutions of the Monge-Ampère equation with the right hand side in Lp

Barbara Brandolini; Barbara Brandolini; Cristina Trombetti; Anna Lisa Amadori

Viscosity solutions of the Monge-Ampère equation with the right hand side in Lp

Barbara Brandolini, Barbara Brandolini, Cristina Trombetti, Anna Lisa Amadori

Matematica e Informatica

Risultato della ricerca: Article › peer review

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.

Lingua originale	English
pagine (da-a)	221-233
Numero di pagine	13
Rivista	ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI
Volume	18
Stato di pubblicazione	Published - 2007

All Science Journal Classification (ASJC) codes

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title = "Viscosity solutions of the Monge-Amp{\`e}re equation with the right hand side in Lp",

abstract = "We compare various notions of solutions of Monge-Amp{\`e}re 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.",

author = "Barbara Brandolini and Barbara Brandolini and Cristina Trombetti and Amadori, {Anna Lisa}",

year = "2007",

language = "English",

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journal = "Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni",

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AU - Trombetti, Cristina

AU - Amadori, Anna Lisa

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AB - 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.

UR - http://hdl.handle.net/10447/494026

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SP - 221

EP - 233

JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

SN - 1120-6330

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