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Estimations of the best constant involving the \(L^ \infty\) norm in Wente’s inequality. (English) Zbl 0869.35032

Summary: We study the best constant in the so-called Wente’s inequality. Our main result relies on the fact that the constant in Wente’s estimate can be bounded from above independently of the domain on which the problem is posed. In particular, if the domain is bounded and simply connected, we show that the best constant involving the \(L^\infty\) norm is \(1/2\pi\).

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
26D10 Inequalities involving derivatives and differential and integral operators
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References:

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