Estimations of the best constant involving the norm in Wente’s inequality and compact -surfaces in euclidean space
ESAIM: Control, Optimisation and Calculus of Variations (1998)
- Volume: 3, page 263-300
- ISSN: 1292-8119
Access Full Article
topHow to cite
topYuxin, 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 3 (1998): 263-300. <http://eudml.org/doc/90524>.
@article{Yuxin1998,
author = {Yuxin, Ge},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {constant mean curvature surfaces; Wente's inequality},
language = {eng},
pages = {263-300},
publisher = {EDP Sciences},
title = {Estimations of the best constant involving the $L^2$ norm in Wente’s inequality and compact $H$-surfaces in euclidean space},
url = {http://eudml.org/doc/90524},
volume = {3},
year = {1998},
}
TY - JOUR
AU - Yuxin, Ge
TI - Estimations of the best constant involving the $L^2$ norm in Wente’s inequality and compact $H$-surfaces in euclidean space
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1998
PB - EDP Sciences
VL - 3
SP - 263
EP - 300
LA - eng
KW - constant mean curvature surfaces; Wente's inequality
UR - http://eudml.org/doc/90524
ER -
References
top- [1] L.V. Ahlfors: Complex analysis, Mcgraw-Hill, NewYork, 1966. Zbl0154.31904MR510197
- [2] T. Aubin: Nonlinear analysis on manifolds, Monge-Ampère equations, Grundlehren, Springer, Berlin-Heidelberg-New York-Tokyo, 252, 1982. Zbl0512.53044MR681859
- [3] S. Baraket: Estimations of the best constant involving the L∞ norm in Wente's inequality, Annales de l'Université Paul Satatier, to appear. Zbl0869.35032
- [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. Zbl0831.35025MR1239099
- [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. Zbl0879.35028MR1340209
- [7] H. Brézis, J.-M. Coron: Multiple solutions of H-Systems and Rellich's conjecture, Comm. Pure. Appl. Math, 37, 1984, 149-187. Zbl0537.49022MR733715
- [8] J.-M. Coron: Topologie et cas limite des injections de Sobolev, C.R. Acad. Sc. Paris, 299, 1984, 209-212. Zbl0569.35032MR762722
- [9] R. Coifman, P.-L. Lions, Y. Meyer, S. Semmes: Compensated compaetness and Hardy spaces, J. Math. Pure, Appl, 72, 1993, 247-286. Zbl0864.42009MR1225511
- [10] J. Eells, J.C. Wood: Restrictions on harmonic maps of surfaces, Topology, 299, 1975, 263-266. Zbl0328.58008MR420708
- [11] L.C. Evans: Weak convergence methods for nonlinear partial differential equations, Regional conference series in mathematics, 74, 1990. Zbl0698.35004MR1034481
- [12] H. Federer: Geometric measure theory, Springer, Berlin and New York, 1969. Zbl0176.00801MR257325
- [13] D. Gilbarg, N.S. Trudinger: Elliptic partial differential equations of second order, Grundlehren, Springer, Berlin-Heidelberg-New York-Tokyo, 224, 1983. Zbl0562.35001MR737190
- [14] P. Hartman, A. Wintner: On the local behavior of solutions of nonparabolic partial differential equations, Amer. J. Math., 75, 1953, 449-476. Zbl0052.32201MR58082
- [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. Zbl0729.49001MR1100926
- [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. Zbl0704.49005MR850686
- [19] M. Struwe: A global compactness resuit for elliptic boundary value problem involving limiting nonlinearities, Math. Z., 26, 1984, 511-517. Zbl0535.35025MR760051
- [20] M. Struwe: Variational Methods, Springer, Berlin-Heidelberg-New York-Tokyo, 1990. Zbl0746.49010MR1078018
- [21] P. Topping: The Optimal Constant in Wente's L∞ Estimate, Comment. Math. Helv., 72, 1997, 316-328. Zbl0892.35030MR1470094
- [22] H. Wente: An existence Theorem for surfaces of constant mean curvature, J. Math. Anal. Appl, 26, 1969, 318-344. Zbl0181.11501MR243467
- [23] H. Wente: The different ial équations ∆x = 2Hxu ʌxv with vanishing boundary values, Proc. AMS, 50, 1975, 131-135. Zbl0313.35030
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.