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References
R. COURANT: The existence of minimal surfaces of given topological structure under prescribed boundary conditions. Acta Math. 72, 51–98 (1940).
R. COURANT: Dirichlet's principle, conformal mapping, and minimal surfaces. Interscience, New York 1950.
G. DZIUK: Über die Stetigkeit teilweise freier Minimalflächen. Manuscripta math. 36, 241–251 (1981).
J. FREHSE: Un problème variationel bidimensionel possédant des extremales bornées et dicontinues. C.R. Acad. Scienc. Paris.
J.D. GERGONNE: Questions proposées. Ann. Math. Pure Appl. 7, 68, 99–100, 156 (1816).
M. GRÜTER: Über die Regularität schwacher Lösungen des Systems Δx=2H(x)xuΓxv. Dissertation, Düsseldorf 1979.
M. GRÜTER: Regularity of weak H-surfaces. Journal für die Reine Angew. Math. 329, 1–15 (1981).
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, 387–410 (1981).
S. HILDEBRANDT, and K.O. WIDMAN: Some regularity results for quasilinear elliptic systems of second order. Math. Z. 142, 67–86 (1975).
S. HILDEBRANDT, and J.C.C. NITSCHE: Minimal surfaces with free boundaries. Acta Math. 143, 251–272 (1979).
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.
S. HILDEBRANDT, and J.C.C. NITSCHE: Optimal boundary regularity for minimal surfaces with a free boundary. Manuscripta math. 33, 357–364 (1981).
S. HILDEBRANDT, and J.C.C. NITSCHE: Geometric properties of minimal surfaces with free boundaries. Preprint (1982).
W. JÄGER: Behavior of minimal surfaces with free boundaries. Comm. Pure Appl. Math. 23, 803–818 (1970).
H. LEWY: On minimal surfaces with partially free boundary. Comm. Pure Appl. Math. 4, 1–13 (1951).
C.B. MORREY: Multiple integrals in the calculus of variations. Springer, Berlin-Heidelberg-New York 1966.
J.C.C. NITSCHE: Vorlesungen über Minimalflächen. Springer, Berlin-Heidelberg-New York 1975.
H.A. SCHWARZ: Fortgesetzte Untersuchungen über spezielle Minimalflächen. Monatsberichte der Königlichen Akad. Wiss. Berlin, 3–27 (1872). Gesammelte Math. Abhandlungen I, 126–148 (1890).
J.E. TAYLOR: The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces. Annals of Math. 103, 489–539 (1976).
J.E. TAYLOR: Boundary regularity for various capillarity and boundary problems. Comm. P.D.E. 2, 323–357 (1977).
K.O. WIDMAN: Hölder continuity of solutions of elliptic systems. Manuscripta math. 5, 299–308 (1971).
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Hildebrandt, S. (1984). Some results on minimal surfaces with free boundaries. In: Vinti, C. (eds) Nonlinear Analysis and Optimization. Lecture Notes in Mathematics, vol 1107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101497
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DOI: https://doi.org/10.1007/BFb0101497
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