Vol. 12, No. 4, 2019

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Nonexistence of Wente's $L^\infty$ estimate for the Neumann problem

Jonas Hirsch

Vol. 12 (2019), No. 4, 1049–1063
DOI: 10.2140/apde.2019.12.1049
Abstract

We provide a counterexample of Wente’s inequality in the context of Neumann boundary conditions. We will also show that Wente’s estimate fails for general boundary conditions of Robin type.

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Keywords
compensated compactness, Jacobian determinants
Mathematical Subject Classification 2010
Primary: 35J05
Secondary: 35J25
Milestones
Received: 19 July 2017
Revised: 15 April 2018
Accepted: 23 July 2018
Published: 20 October 2018
Authors
Jonas Hirsch
Scuola Internazionale Superiore di Studi Avanzati
Trieste
Italy