Baraket, Sami Estimations of the best constant involving the \(L^ \infty\) norm in Wente’s inequality. (English) Zbl 0869.35032 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 5, No. 3, 373-385 (1996). 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 \(1/2\pi\). Cited in 1 ReviewCited in 10 Documents MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 26D10 Inequalities involving derivatives and differential and integral operators Keywords:best constant in Wente’s inequality PDFBibTeX XMLCite \textit{S. Baraket}, Ann. Fac. Sci. Toulouse, Math. (6) 5, No. 3, 373--385 (1996; Zbl 0869.35032) Full Text: DOI Numdam EuDML References: [1] Bethuel, F.) and Ghidaglia, J.-M.) .- Improved regularity of elliptic equations involving jacobians and applications, J. Math. Pures Appl. (to appear). · Zbl 0831.35025 [2] Bethuel, F.) and Ghidaglia, J.-M.) .- Some applications of the coarea formula to partial differential equations, (to appear). · Zbl 0879.35028 [3] Brezis, H.) and Coron, J.-M.) .- Multiple solutions of H-systems and Rellich’s conjecture, Comm. Pure Appl. Math.37 (1984), pp. 149-187. · Zbl 0537.49022 [4] Gilbarg, D.) and Trudinger, N.S.) .- Elliptic partial differential equations of second order, 2nd Edition Springer-Verlag (1984). · Zbl 0562.35001 [5] Wente, H.) .- An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl.26 (1969), pp. 318-344. · Zbl 0181.11501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.