Finn, Robert Local and global existence criteria for capillary surfaces in wedges. (English) Zbl 0872.76017 Calc. Var. Partial Differ. Equ. 4, No. 4, 305-322 (1996). (Author’s introduction.) This paper addresses a conjecture of P. Concus and R. Finn [SIAM J. Math. Anal. 27, No. 1, 56-69 (1996; Zbl 0843.76012)] on conditions for local existence of solutions of the zero-gravity capillarity equation at a boundary protruding corner point \(P\) of prescribed opening angle \(2\alpha\). Geometrically, surfaces of constant mean curvature \(H\) are sought as graphs which meet vertical walls over the boundary in prescribed angles, which are locally constant except for a possible jump discontinuity at \(P\). The conjecture is settled more or less completely in the affirmative manner, depending on whether \(H\) is to be prescribed. The proof proceeds through a global existence theorem for “moon domains”, which seems to be of independent interest. Reviewer: E.Miersemann (Leipzig) Cited in 5 Documents MSC: 76B45 Capillarity (surface tension) for incompressible inviscid fluids 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 49Q10 Optimization of shapes other than minimal surfaces 53C80 Applications of global differential geometry to the sciences Keywords:contact angle; moon domains; zero-gravity capillarity equation; boundary protruding corner point; constant curvature Citations:Zbl 0843.76012 PDFBibTeX XMLCite \textit{R. Finn}, Calc. Var. Partial Differ. Equ. 4, No. 4, 305--322 (1996; Zbl 0872.76017) Full Text: DOI References: [1] Chen, J.-T., E. Miersemann: On capillary surfaces in wedge domains (In preparation) [2] Chua, K.-S.: Absolute gradient bounds for surfaces of constant mean curvature. Ann. Scuola Normale Sup. Pisa21, 1–9 (1994) [3] Concus, P., R. Finn: On capillary free surfaces in the absence of gravity. Acta Math.132, 177–198 (1974) · Zbl 0382.76003 [4] Concus, P., R. Finn: Capillary Wedges Revisited. SIAM J. Math. Anal. (in press) · Zbl 0843.76012 [5] Evans, L.C., R.F. Gariepy: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. Boca Raton: CRC Press 1992 · Zbl 0804.28001 [6] Finn, R.: Equilibrium Capillary Surfaces. Grundlehren Math. Wiss., Bd. 284, Springer, Berlin Heidelberg New York, 1986 · Zbl 0583.35002 [7] Finn, R.: Moon Surfaces, and Boundary Behavior of Capillary Surfaces for Perfect Wetting and Non-Wetting. Proc. Lon. Math. Soc.57, 542–576 (1988) · Zbl 0668.76019 [8] Finn, R.: On a result of Lancaster and Siegel. Pac. J. Math. (to appear) · Zbl 1156.76361 [9] Finn, R., E. Giusti: On nonparametric surfaces of constant mean curvature. Ann. Scuola Normale Sup. Pisa4, 13–31 (1977) · Zbl 0343.53004 [10] Giusti, E.: Boundary value problems for non-parametric surfaces of prescribed mean curvature. Ann. Scuola Norm. Sup. Pisa3, 501–548 (1976) · Zbl 0344.35036 [11] Giusti, E.: Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston Basel Stuttgart, 1984 · Zbl 0545.49018 [12] Jenkins, H., J.B. Serrin: Variational Problems of Minimal Surface Type: II. Boundary Value Problems for the Minimal Surface Equation. Arch. Rat. Mech. Anal.21, 321–342 (1966) · Zbl 0171.08301 [13] Lancaster, K.E., D. Siegel: Radial Limits of Capillary Surfaces. Pac. J. Math. (to appear) · Zbl 1361.35030 [14] Liang, F.-T.: An absolute gradient bound for nonparametric surfaces of constant mean curvature. Ind. Univ. Math. J.41, 569–604 (1992) · Zbl 0837.53049 [15] Massari, U., M. Miranda: Minimal Surfaces of Codimension One. (North Holland Mathematics Studies 91), Elsevier Science Publ., Amsterdam 1984 · Zbl 0565.49030 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.