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
Primary: 35J05
Secondary: 35J25