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.
Accepté le :
Publié le :
@article{CRMATH_2002__335_7_597_0, author = {Matei, Ana-Maria}, title = {The {Neumann} problem for free boundaries in two dimensions}, journal = {Comptes Rendus. Math\'ematique}, pages = {597--602}, publisher = {Elsevier}, volume = {335}, number = {7}, year = {2002}, doi = {10.1016/S1631-073X(02)02530-X}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02530-X/} }
TY - JOUR AU - Matei, Ana-Maria 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 UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02530-X/ DO - 10.1016/S1631-073X(02)02530-X LA - en ID - CRMATH_2002__335_7_597_0 ER -
%0 Journal Article %A Matei, Ana-Maria %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 %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02530-X/ %R 10.1016/S1631-073X(02)02530-X %G en %F CRMATH_2002__335_7_597_0
Matei, Ana-Maria. The Neumann problem for free boundaries in two dimensions. Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 597-602. doi : 10.1016/S1631-073X(02)02530-X. http://www.numdam.org/articles/10.1016/S1631-073X(02)02530-X/
[1] 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] On the Stokes conjecture for the wave of extreme form, Acta Math., Volume 148 (1982), pp. 193-214
[3] Regularity in free boundary value problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) (1977), pp. 373-391
[4] Regularity in elliptic free boundary problems I, J. Anal. Math., Volume 34 (1978), pp. 86-119
[5] Regularity in elliptic free boundary problems II; Equations of higher order, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) (1979), pp. 637-683
[6] A note on harmonic functions and a hydrodynamical application, Proc. Amer. Math. Soc., Volume 3 (1952), pp. 111-113
[7] Multiple Integrals in the Calculus of Variations, Springer, New York, 1966
Cité par Sources :