Nonexistence of Wente’s L∞ estimate for the Neumann problem

Hirsch, Jonas

doi:10.2140/apde.2019.12.1049

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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

Vol. 12, No. 4, 2019