Vertex theorems for capillary drops on support planes

Mathematische Nachrichten

Volumn 209, Issue , 2000, Pages 115-135

  Finn, Robert ^a   McCuan, John ^b,c  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

Author keywords

Capillarity; Liquid drops; Mean curvature; Polyhedral angles; Wedges

Indexed keywords

EID: 0000073082     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1522-2616(200001)209:1<115::AID-MANA115>3.0.CO;2-J     Document Type: Article

References (31)

1. ALEXANDROV, A. D.: Uniqueness Theorems for Surfaces in the Large. V, Vestnik Leningrad Univ. 13 (1958), 5-24, Amer. Math. Soc. Translations (Series 2) 21, 412-416
2. ALEXANDROV, A. D.: Uniqueness Theorems for Surfaces in the Large. V, Vestnik Leningrad Univ. 13 (1958), 5-24, Amer. Math. Soc. Translations (Series 2) 21, 412-416
3. AMBRAZEVIČIUS, A. P.: Solvability of a Problem on a Conic Capillary. In: Partial Differential Equations. Spectral Theory, Probl. Mat. Anal. 221 (1981), 3-22, Leningrad, Russian
4. AMBRAZEVIČIUS, A. P.: Finding the Form of the Surface of a Liquid in a Conical Container for a Given Volume of the Liquid I, Lithuanian Math. J. 22 (1982), 1-6
5. AZZAM, A.: Behaviour of Solutions of Dirichlet Problem for Elliptic Equations at a Corner, Indian J. Pure Appl. Math. 10 (1979), 1453-1459
6. CHEN, J.-T., FINN, R., and MIERSEMANN, E.: Capillary Surfaces in Wedge Domains: Behavior at the Vertex, Continuity and Discontinuity, Asymptotic Expansions, Preprint, Universität Leipzig, 1997
7. CONCUS, P., and FINN, R.: Capillary Wedges Revisited, SIAM J. Math. Anal. 27 (1996), 56-69
8. COURANT, R., and HILBERT, D.: Methods of Mathematical Physics Vol. II, pp. 350, Interscience, 1962
9. FINN, R.: Equilibrium Capillary Surfaces, Springer-Verlag, New York, 1986
10. FINN, R.: Local and Global Existence Criteria for Capillary Surfaces in Wedges, Calc. Var. 4 (1996), 305-322
11. GERHARDT, C.: Global Regularity of Solutions to the Capillarity Problem, 3 (1976), 157-175
12. GERHARDT, C.: Boundary Value Problems for Surfaces of Prescribed Mean Curvature, J. Math. Pures Appl. 58 (1979), 75-109
13. HOPF, H.: Über Flächen, mit einer Relation zwischen den Hauptkrümmungen, Math. Nachr. 4 (1951), 232-249
14. HOPF, H.: Differential Geometry in the Large, Lecture Notes in Mathematics No. 1000 (1989), Springer-Verlag, Berlin
15. JOACHIMSTHAL, F.: Demonstrationes theorematum ad superficies curvas spectantium, J. reine angew. Math. 30 (1846), 347-350
16. KONTRAT'EV, V. A.: The Smoothness of a Solution of Dirichlet's Problem for Second Order Elliptic Equations in a Region with a Piecewise-Smooth Boundary, Differential Equations 6 (1970), 1831-1843, English translation 1392-1401
17. KONTRAT'EV, V. A.: Singularities of a Solution of Dirichlet's Problem for a Second Order Elliptic Equation in the Neighborhood of an Edge, Differential Equations 13 (1977), 2026-2032, English translation 1411-1415
18. LANCASTER, K. E., and SIEGEL, D.: Radial Limits of Capillary Surfaces, Pacific J. Math.
19. LIEBERMAN, G.: Hölder Continuity of the Gradient at a Corner for the Capillary Problem and Related Results, Pacific J. Math. 133 (1988), 115-135
20. MAZ'YA, V. G., and PLAMENEVSKII, B. A.: Schauder Estimates of Solutions of Elliptic Boundary Value Problems in Domains with Edges on the Boundary, Proc. Sem. S. L. Sobolev, 69-1023, Novosibirsk, 1978, English translation: Elliptic Boundary Value Problems, AMS Translations, 123 (1984), 141-170
21. MAZ'YA, V. G., and PLAMENEVSKII, B. A.: Schauder Estimates of Solutions of Elliptic Boundary Value Problems in Domains with Edges on the Boundary, Proc. Sem. S. L. Sobolev, 69-1023, Novosibirsk, 1978, English translation: Elliptic Boundary Value Problems, AMS Translations, 123 (1984), 141-170
22. MCCUAN, J.: Symmetry via Spherical Reflection and Spanning Drops in a Wedge, Pacific J. Math. 180 (1997), 291-323
23. MIERSEMANN, E.: On the Behavior of Capillaries in a Corner, Pacific J. Math. 157 (1989), 149-153
24. NITSCHE, J. C. C.: Stationary Partitioning of Convex Bodies, Arch. Rat. Mech. An. 89 (1985), 1-19
25. SIEGEL, D.: Height Estimates for Capillary Surfaces, Pacific J. Math. 88 (1980), 471-516
26. SIMON, L.: Regularity of Capillary Surfaces over Domains with Corners, Pacific J. Math. 88 (1980), 363-377
27. TAM, L.-F.: Regularity of Capillary Surfaces over Domains with Corners: Borderline Case, Pacific J. Math. 124 (1986), 469-482
28. URAL'TSEVA, N. N.: Solution of the Capillary Problem, Vestnik Leningrad Univ. 19 (1973), 54-64, Russian
29. VOGEL, T. I.: Uniqueness of Capillary Surfaces in Wedges and Cones. In: Geometric Analysis and Nonlinear Partial Differential Equations (Denton, TX, 1990), Lecture Notes in Pure and Appl. Math. 144 (1993), 129-138, Dekker, New York
30. WENTE, H. C.: The Symmetry of Sessile and Pendant Drops, Pacific J. Math. 88 (1980), 387-397
31. WENTE, H. C.: Tubular Capillary Surfaces in a Convex Body. In: PAUL CONCUS, K. LANCASTER (Eds.), Advances in Geometric Analysis and Continuum Mechanics, 288-298, International Press, 1993 (1995)