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Nonexistence of Wente’s \(L^\infty\) estimate for the Neumann problem. (English) Zbl 1405.35023
Author’s 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.

MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
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