The Neumann problem for free boundaries in two dimensions

Ana-Maria Matei

doi:10.1016/S1631-073X(02)02530-X

The Neumann problem for free boundaries in two dimensions
[Le problème de Neumann pour les frontières libres en deux dimensions]

Ana-Maria Matei ¹

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

Abstract (VO)
Résumé

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.

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.

Reçu le : 2002-07-25
Accepté le : 2002-08-09
Publié le : 2002-09-11

DOI : 10.1016/S1631-073X(02)02530-X

Affiliations des auteurs :

Ana-Maria Matei ¹

¹ McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, On L8S 4K1, Canada

@article{CRMATH_2002__335_7_597_0,
     author = {Ana-Maria Matei},
     title = {The {Neumann} problem for free boundaries in two dimensions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {597--602},
     year = {2002},
     publisher = {Elsevier},
     volume = {335},
     number = {7},
     doi = {10.1016/S1631-073X(02)02530-X},
     language = {en},
}

TY  - JOUR
AU  - Ana-Maria Matei
TI  - The Neumann problem for free boundaries in two dimensions
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 597
EP  - 602
VL  - 335
IS  - 7
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02530-X
LA  - en
ID  - CRMATH_2002__335_7_597_0
ER  -

%0 Journal Article
%A Ana-Maria Matei
%T The Neumann problem for free boundaries in two dimensions
%J Comptes Rendus. Mathématique
%D 2002
%P 597-602
%V 335
%N 7
%I Elsevier
%R 10.1016/S1631-073X(02)02530-X
%G en
%F CRMATH_2002__335_7_597_0

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

Bibliographie
Cité par

[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

Cité par Sources :

Commentaires - Politique