Capillary surfaces at a reentrant corner

Pacific Journal of Mathematics

Volumn 224, Issue 2, 2006, Pages 321-353

  Shi , D ^a  

^a NONE

Author keywords

Capillary surfaces; Concus Finn conjecture; Corner behavior; Reentrant corner

Indexed keywords

EID: 36849004700     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2006.224.321     Document Type: Article

References (21)

1. J.-T. Chen, R. Finn, and E. Miersemann, "Capillary surfaces in wedge domains: behavior at the vertex, continuity and discontinuity, asymptotic expansions", preprint, Univ. Leipzig, 1998.
2. P. Concus and R. Finn, "On capillary free surfaces in a gravitational field", Acta Math. 132 (1974), 207-223. MR 58 #32327c Zbl 0382.76005
3. P. Concus and R. Finn, "On capillary free surfaces in the absence of gravity", Acta Math. 132 (1974), 177-198. MR 58 #32327a Zbl 0382.76003
4. P. Concus and R. Finn, "Capillary surfaces in a wedge: differing contact angles", Microgravity Sci. Tech. 7 (1994), 152-155.
5. P. Concus and R. Finn, "Capillary wedges revisited", SIAM J. Math. Anal. 27:1 (1996), 56-69. MR 96m:76006 Zbl 0843.76012
6. M. Emmer, "Esistenza, unicità e regolarità nelle superfici de equilibrio nei capillari", Ann. Univ. Ferrara Sez. VII (N.S.) 18 (1973), 79-94. MR 49 #1281 Zbl 0275.49005
7. R. Finn, "A note on the capillary problem", Acta Math. 132 (1974), 199-205. MR 58 #32327b Zbl 0382.76004
8. R. Finn, "Equilibrium capillary surfaces", Grundlehren der Math. Wissenschaften 284, Springer, New York, 1986. MR 88f:49001 Zbl 0583.35002
9. R. Finn and C. Gerhardt, "The internal sphere condition and the capillary problem", Ann. Mat. Pura Appl. (4) 112 (1977), 13-31. MR 55 #7106 Zbl 0349.49019
10. E. Giusti, Minimal surfaces and functions of bounded variation, Department of Pure Mathematics, Australian National University, Canberra, 1977. MR 58 #30685 Zbl 0402.49033
11. W. E. Johnson and L. M. Perko, "Interior and exterior boundary value problems from the theory of the capillary tube", Arch. Rational Mech. Anal. 29 (1968), 125-143. MR 36 #6686 Zbl 0162.57002
12. N. J. Korevaar, "On the behavior of a capillary surface at a re-entrant corner", Pacific J. Math. 88:2 (1980), 379-385. MR 82c:49033 Zbl 0475.49034
13. K. E. Lancaster and D. Siegel, "Existence and behavior of the radial limits of a bounded capillary surface at a corner", Pacific J. Math. 176:1 (1996), 165-194. MR 98g:58030a Zbl 0866.76018
14. G. M. Lieberman, "Hölder continuity of the gradient at a corner for the capillary problem and related results", Pacific J. Math. 133 (1988), 115-135. MR89h:35050 Zbl 0669.35034
15. U. Massari and L. Pepe, "Successioni convergenti di ipersuperfici di curvatura media assegnata", Rend. Sem Mat. Univ. Padova 53 (1975), 53-68. MR 54 #8415 Zbl 0358.49020
16. E. Miersemann, "On capillary free surfaces without gravity", Z. Anal. Anwendungen 4:5 (1985), 429-436. MR 87i:49058 Zbl 0581.35023
17. M. Miranda, "Superfici cartesiane generalizzate ed insiemi di perimetro localmente finito sui prodotti cartesiani", Ann. Scuola Norm. Sup. Pisa (3) 18 (1964), 515-542. MR 30 #4906 Zbl 0152.24402
18. D. Shi and R. Finn, "On a theorem of Lancaster and Siegel", Pacific J. Math. 213:1 (2004), 111-119. MR 2004m:76038 Zbl 02101146
19. L. Simon, "Regularity of capillary surfaces over domains with corners", Pacific J. Math. 88:2 (1980), 363-377. MR 82d:49043 Zbl 0467.35022
20. L.-F. Tam, "The behavior of capillary surfaces as gravity tends to zero", Comm. Partial Differential Equations 11:8 (1986), 851-901. MR 89c:76040 Zbl 0607.35041
21. L.-F. Tam, "Regularity of capillary surfaces over domains with corners: borderline case", Pacific J. Math. 124:2 (1986), 469-482. MR 87k:49049 Zbl 0604.49029