Remarks on Neumann boundary problems involving Jacobians
Francesca Da Lio, Francesco Palmurella
TL;DR
This paper investigates the applicability of Wente-type estimates to Neumann boundary problems involving Jacobians, revealing that these estimates do not generally hold under similar conditions as Dirichlet problems.
Contribution
It demonstrates that Wente-type estimates valid for Dirichlet problems fail for Neumann boundary problems involving Jacobians under comparable assumptions.
Findings
Wente-type estimates do not generally hold for Neumann problems
Differences between Dirichlet and Neumann boundary conditions affect estimate validity
Highlights limitations of existing estimates in boundary value problem analysis
Abstract
In this short note we explore the validity of Wente-type estimates for Neumann boundary problems involving Jacobians. We show in particular that such estimates do not in general hold under the same hypotheses on the data for Dirichlet boundary problems.
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