Estimations of the best constant involving the L 2 norm in Wente’s inequality and compact H-surfaces in euclidean space
ESAIM: Control, Optimisation and Calculus of Variations, Tome 3 (1998), pp. 263-300. 
@article{COCV_1998__3__263_0,
     author = {Yuxin, Ge},
     title = {Estimations of the best constant involving the $L^2$ norm in {Wente{\textquoteright}s} inequality and compact $H$-surfaces in euclidean space},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {263--300},
     publisher = {EDP-Sciences},
     volume = {3},
     year = {1998},
     mrnumber = {1634837},
     zbl = {0903.53003},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1998__3__263_0/}
}
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Yuxin, Ge. Estimations of the best constant involving the $L^2$ norm in Wente’s inequality and compact $H$-surfaces in euclidean space. ESAIM: Control, Optimisation and Calculus of Variations, Tome 3 (1998), pp. 263-300. http://www.numdam.org/item/COCV_1998__3__263_0/

[1] L.V. Ahlfors: Complex analysis, Mcgraw-Hill, NewYork, 1966. | MR | Zbl

[2] T. Aubin: Nonlinear analysis on manifolds, Monge-Ampère equations, Grundlehren, Springer, Berlin-Heidelberg-New York-Tokyo, 252, 1982. | MR | Zbl

[3] S. Baraket: Estimations of the best constant involving the L∞ norm in Wente's inequality, Annales de l'Université Paul Satatier, to appear. | Numdam | Zbl

[4] F. Bethuel: Méthodes géométriques et topologiques en EDP, Majeure de mathématiques, Ecole polytechnique.

[5] F. Bethuel, J.-M. Ghidaglia: Improved regularity of elliptic equations involving jacobians and applications, J. Math. Pure. Appl., 72, 1993, 441-475. | MR | Zbl

[6] F. Bethuel, J.-M. Ghidaglia: Some applications of the coarea formula to partial differential equations, in Geometry in Partial differential Equation, A. Pratano and T. Rassias Ed., World Scientific Publication. | MR | Zbl

[7] H. Brézis, J.-M. Coron: Multiple solutions of H-Systems and Rellich's conjecture, Comm. Pure. Appl. Math, 37, 1984, 149-187. | MR | Zbl

[8] J.-M. Coron: Topologie et cas limite des injections de Sobolev, C.R. Acad. Sc. Paris, 299, 1984, 209-212. | MR | Zbl

[9] R. Coifman, P.-L. Lions, Y. Meyer, S. Semmes: Compensated compaetness and Hardy spaces, J. Math. Pure, Appl, 72, 1993, 247-286. | MR | Zbl

[10] J. Eells, J.C. Wood: Restrictions on harmonic maps of surfaces, Topology, 299, 1975, 263-266. | MR | Zbl

[11] L.C. Evans: Weak convergence methods for nonlinear partial differential equations, Regional conference series in mathematics, 74, 1990. | MR | Zbl

[12] H. Federer: Geometric measure theory, Springer, Berlin and New York, 1969. | MR | Zbl

[13] D. Gilbarg, N.S. Trudinger: Elliptic partial differential equations of second order, Grundlehren, Springer, Berlin-Heidelberg-New York-Tokyo, 224, 1983. | MR | Zbl

[14] P. Hartman, A. Wintner: On the local behavior of solutions of nonparabolic partial differential equations, Amer. J. Math., 75, 1953, 449-476. | MR | Zbl

[15] F. Hélein: Applications harmoniques, lois de conservation et repère mobile, Diderot éditeur, Paris-New York-Amsterdam, 1996, or Harmonic maps, conservation laws and moving frames, Diderot éditeur, Paris-New York-Amsterdam, 1997.

[16] J. Jost: Two-dimensional geometric variational problems, Wiley, 1991. | MR | Zbl

[17] Y.M. Koh: Variational problems for surfaces with volume constraint, PhD Thesis, University of Southern California, 1992.

[18] P.-L. Lions: The concentration-compactness principle in the calculus of variations: The limit case. Part I and Part II, Rev. Mat. Ibero., 1(1), 1985, 145-201 and 1(2), 1985, 45-121. | MR | Zbl

[19] M. Struwe: A global compactness resuit for elliptic boundary value problem involving limiting nonlinearities, Math. Z., 26, 1984, 511-517. | MR | Zbl

[20] M. Struwe: Variational Methods, Springer, Berlin-Heidelberg-New York-Tokyo, 1990. | MR | Zbl

[21] P. Topping: The Optimal Constant in Wente's L∞ Estimate, Comment. Math. Helv., 72, 1997, 316-328. | MR | Zbl

[22] H. Wente: An existence Theorem for surfaces of constant mean curvature, J. Math. Anal. Appl, 26, 1969, 318-344. | MR | Zbl

[23] H. Wente: The different ial équations ∆x = 2Hxu ʌxv with vanishing boundary values, Proc. AMS, 50, 1975, 131-135. | Zbl