Comptes Rendus
no. 7
The Neumann problem for free boundaries in two dimensions
[Le problème de Neumann pour les frontières libres en deux dimensions]
Ana-Maria Matei1
1 McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, On L8S 4K1, Canada
Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 597-602.

Nous généralisons au cas avec tension superficielle un résultat de H. Lewy concernant la régularité a priori des solutions en ondes progressives pour le problème d'écoulements à surface libre.

We extend to the case with surface tension a theorem of H. Lewy concerning the a priori regularity of traveling waves solutions of the free surface problem of water waves.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02530-X
Ana-Maria Matei 1

1 McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, On L8S 4K1, Canada 
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Ana-Maria Matei. The Neumann problem for free boundaries in two dimensions. Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 597-602. doi : 10.1016/S1631-073X(02)02530-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02530-X/

[1] S. Agmon; A. Douglis; L. Nirenberg Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math., Volume 12 (1959), pp. 623-727

[2] C.J. Amick; L.E. Fraenkel; J.F. Toland On the Stokes conjecture for the wave of extreme form, Acta Math., Volume 148 (1982), pp. 193-214

[3] D. Kinderlehrer; L. Nirenberg Regularity in free boundary value problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) (1977), pp. 373-391

[4] D. Kinderlehrer; L. Nirenberg; J. Spruck Regularity in elliptic free boundary problems I, J. Anal. Math., Volume 34 (1978), pp. 86-119

[5] D. Kinderlehrer; L. Nirenberg; J. Spruck Regularity in elliptic free boundary problems II; Equations of higher order, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) (1979), pp. 637-683

[6] H. Lewy A note on harmonic functions and a hydrodynamical application, Proc. Amer. Math. Soc., Volume 3 (1952), pp. 111-113

[7] C.B. Morrey Multiple Integrals in the Calculus of Variations, Springer, New York, 1966

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