Global regularity of the solutions to the capillarity problem

Claus Gerhardt

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1976)

  • Volume: 3, Issue: 1, page 157-175
  • ISSN: 0391-173X

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Gerhardt, Claus. "Global regularity of the solutions to the capillarity problem." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.1 (1976): 157-175. <http://eudml.org/doc/83710>.

@article{Gerhardt1976,
author = {Gerhardt, Claus},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {157-175},
publisher = {Scuola normale superiore},
title = {Global regularity of the solutions to the capillarity problem},
url = {http://eudml.org/doc/83710},
volume = {3},
year = {1976},
}

TY - JOUR
AU - Gerhardt, Claus
TI - Global regularity of the solutions to the capillarity problem
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1976
PB - Scuola normale superiore
VL - 3
IS - 1
SP - 157
EP - 175
LA - eng
UR - http://eudml.org/doc/83710
ER -

References

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  1. [1] E. Bombieri - E. Giusti, Local estimates for the gradient of non-parametric surfaces of prescribed mean curvature, Comm. Pure Appl. Math., 26 (1973), pp. 381-394. Zbl0266.53042MR344977
  2. [2] P. Concus - R. Finn, On capillary free surfaces in a gravitational field, Acta Math., 132 (1974), pp. 207-223. Zbl0382.76005MR670443
  3. [3] C. Gerhardt, Existence, regularity, and boundary behaviour of generalized surfaces of prescribed mean curvature, Math. Z., 139 (1974), pp. 173-198. Zbl0316.49005MR437925
  4. [4] C. Gerhardt, On the capillarity problem with constant volume, Ann. Sc. Norm. Sup. Pisa, S. IV, 2 (1975), pp. 303-320. Zbl0321.76010MR390897
  5. [5] C. Gerhardt, Hypersurfaces of prescribed mean curvature over obstacles, Math. Z., 133 (1973), pp. 169-185. Zbl0265.35027MR324528
  6. [6] C. Gerhardt, Existence and regularity of capillary surfaces, Boll. U.M.I., 10 (1974), pp. 317-335. Zbl0314.49019MR365316
  7. [7] O.A. Ladyzhenskaya - N.N. Ural'ceva, Linear and quasilinear elliptic equations, New York-London, Academic Press (1968). Zbl0164.13002MR244627
  8. [8] O.A. Ladyzhenskaya - N.N. Ural'ceva, Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations, Comm. Pure Appl. Math., 23 (1969), pp. 677-703. Zbl0193.07202MR265745
  9. [9] J.H. Michael - L.M. Simon, Sobolev and mean-value inequalities on generalized submanifolds of Rn, Comm. Pure Appl. Math., 26 (1973), pp. 361-379. Zbl0256.53006MR344978
  10. [10] M. Schechter, On Lp estimates and regularity, I, Am. J. Math., 85 (1963), pp. 1-13. Zbl0113.30603MR188615
  11. [11] L.M. Simon - J. Spruck, Existence and regularity of a capillary surface with prescribed contact angle, to appear. Zbl0361.35014
  12. [12] J. Spruck, On the existence of a capillary surface with prescribed contact angle, Comm. Pure Appl. Math., to appear. Zbl0297.76018MR398278
  13. [13] N.S. Trudinger, Gradient estimates and mean curvature, Math. Z., 131 (1973), pp. 165-175. Zbl0253.53003MR324187
  14. [14] N.N. Ural'ceva, Nonlinear boundary value problems for equations of minimal surface type, Proc. Steklov Inst. Math., 116 (1971), pp. 227-237. Zbl0232.35042MR364860
  15. [15] N.N. Ural'ceva, The solvability of the capillarity problem, Vestnik Leningrad Univ. No. 19 Mat. Meh. Astronom. Vyp., 4 (1973), pp. 54-64, Russian. MR638359

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