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.

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