Minimal surfaces with free boundaries and related problems
Variational methods for equilibrum problems of fluids - Trento, 20-25 juin 1983, Astérisque no. 118  (1984), p. 69-88
@incollection{AST_1984__118__69_0,
     author = {Hildebrandt, S.},
     title = {Minimal surfaces with free boundaries and related problems},
     booktitle = {Variational methods for equilibrum problems of fluids - Trento, 20-25 juin 1983},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {118},
     year = {1984},
     pages = {69-88},
     zbl = {0569.53004},
     mrnumber = {761738},
     language = {en},
     url = {http://www.numdam.org/item/AST_1984__118__69_0}
}
Hildebrandt, S. Minimal surfaces with free boundaries and related problems, in Variational methods for equilibrum problems of fluids - Trento, 20-25 juin 1983, Astérisque, no. 118 (1984), pp. 69-88. http://www.numdam.org/item/AST_1984__118__69_0/

[1] R. Courant, The existence of minimal surfaces of given topological structure under prescribed boundary conditions. Acta Math. 72 (1940), 51-98. | Article | JFM 66.0485.02 | MR 2478

[2] R. Courant, Dirichlet's principle, conformai mapping, and minimal surfaces. Interscience, New York, 1950. | MR 36317 | Zbl 0040.34603 | Zbl 0354.30012

[3] G. Dziuk, Über die Stetigkeit teilweise freier Minimalflächen, Manuscripta math. 36 (1981), 241-251. | Article | MR 641976 | Zbl 0468.49023

[4] J. Frehse, Un problème variationel bidimensionel possédant des extremales bornées et dicontinues, C.R. Acad. Scienc. Paris. | Zbl 0423.35001

[5] J. D. Gergonne, Questions proposées, Ann. Math. Pure Appl. 7, 68, 156 (1816), 99-100. | MR 1555884

[6] M. Gruter, Über die Regularität schwacher Losungen des Systems Δx=2H(x)s u x v , Dissertation, Düsseldorf, 1979.

[7] M. Gruter, Regularity of weak H-surfaces, Journal für die Reine Angew. Math. 329 (1981), 1-15. | MR 636440 | Zbl 0461.53029

[8] M. Grüter, S. Hildebrandt and J. C. C. Nitsche, On the boundary behavior of minimal surfaces with a free boundary which are not minima of the area, Manuscripta math. 35. (1981), 387-410. | Article | MR 636464 | Zbl 0483.49037

[9] M. Grüter, S. Hildebrandt and J. C. C. Nitsche, Regularity for stationary surfaces of constant mean curvature with free boundaries, Manuscript. | Article | Zbl 0609.49027

[10] S. Hildebrandt and K.-O. Widman, Some regularity results for quasilinear elliptic systems of second order, Math. Z. 142 (1975), 67-86. | Article | MR 377273 | Zbl 0317.35040

[11] S. Hildebrandt and J. C. C. Nitsche, Minimal surfaces with free boundaries, Acta Math. 143 (1979), 251-272. | Article | MR 549778 | Zbl 0444.49035

[12] S. Hildebrandt and J. C. C. Nitsche, A uniqueness theorem for surfaces of least area with partially free boundaries on obstacles, to appear in Archive for Rat. Mech. Analysis. | MR 658387 | Zbl 0506.49017

[13] S. Hildebrandt and J. C. C. Nitsche, Optimal boundary regularity for minimal surfaces with a free boundary, Manuscripta math. 33 (1981), 357-364. | Article | MR 612618 | Zbl 0465.49029

[14] S. Hildebrandt and J. C. C. Nitsche, Geometric properties of minimal surfaces with free boundaries, to appear in Math. Z. | MR 719490 | Zbl 0505.49020

[15] A. Küster, The optimal version of Hildebrandt's and Nitsche's estimate of the length of the trace of a minimal surface with a partially free boundary. Preprint, 1983.

[16] H. Lewy, On minimal surfaces with partially free boundary. Comm. Pure Appl. Math. 4 (1951), 1-13. | Article | MR 52711

[17] C. B. Morrey, Multiple integrals in the calculus of variations. Springer, Berlin-Heidelberg-New York, 1966. | MR 202511 | Zbl 0142.38701

[18] J. C. C. Nitsche, Vorlesungen über Minimalflächen, Springer, Berlin-Heidelberg-New York, 1975. | MR 448224 | Zbl 0319.53003

[19] H. A. Schwarz, Fortgesetzte Untersuchungen über spezielle Minimalflächen, Monatsberichte der Königlichen Akad. Wiss. Berlin (1872), 3-27. | JFM 05.0412.02

H. A. Schwarz, Fortgesetzte Untersuchungen über spezielle Minimalflächen, Gesammelte Math. Abhandlungen I (1890), 126-148. | Article

[20] J. E. Taylor, The structure of singularities in soap-bubble-like and soap-film-­like minimal surfaces, Annals of Math. 103 (1976), 489-539. | Article | MR 428181 | Zbl 0335.49032

[21] J. E. Taylor, Boundary regularity for various capillarity and boundary problems. Comm. P.D.E. 2 (1977), 323-357. | Article | MR 487721 | Zbl 0357.35010

[22] K.-O. Widman, Hölder continuity of solutions of elliptic systems, Manuscripta math. 5 (1971), 299-308. | Article | MR 296484 | Zbl 0223.35044