Minimal surfaces with free boundaries and related problems
Variational methods for equilibrum problems of fluids - Trento, 20-25 juin 1983, Astérisque, no. 118 (1984), pp. 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},
     series = {Ast\'erisque},
     pages = {69--88},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {118},
     year = {1984},
     mrnumber = {761738},
     zbl = {0569.53004},
     language = {en},
     url = {http://www.numdam.org/item/AST_1984__118__69_0/}
}
TY  - CHAP
AU  - Hildebrandt, S.
TI  - Minimal surfaces with free boundaries and related problems
BT  - Variational methods for equilibrum problems of fluids - Trento, 20-25 juin 1983
AU  - Collectif
T3  - Astérisque
PY  - 1984
SP  - 69
EP  - 88
IS  - 118
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1984__118__69_0/
LA  - en
ID  - AST_1984__118__69_0
ER  - 
%0 Book Section
%A Hildebrandt, S.
%T Minimal surfaces with free boundaries and related problems
%B Variational methods for equilibrum problems of fluids - Trento, 20-25 juin 1983
%A Collectif
%S Astérisque
%D 1984
%P 69-88
%N 118
%I Société mathématique de France
%U http://www.numdam.org/item/AST_1984__118__69_0/
%G en
%F AST_1984__118__69_0
Hildebrandt, S. Minimal surfaces with free boundaries and related problems, dans 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. | DOI | JFM | MR

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

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

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

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

[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. | EuDML | MR | Zbl

[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. | DOI | EuDML | MR | Zbl

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

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

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

[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 | Zbl

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

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

[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. | DOI | MR

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

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

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

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

[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. | DOI | MR | Zbl

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

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