Nonexistence of some nonparametric surfaces of prescribed mean curvature
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- by Kirk E. Lancaster PDF
- Proc. Amer. Math. Soc. 96 (1986), 187-188 Request permission
Abstract:
If $\Omega \subset {{\mathbf {R}}^2}$ has a reentrant corner, the Dirichlet problem for the equation of prescribed mean curvature $H$ with zero boundary value has no solution when $H$ has constant nonzero sign.References
- Alan R. Elcrat and Kirk E. Lancaster, Boundary behavior of a nonparametric surface of prescribed mean curvature near a reentrant corner, Trans. Amer. Math. Soc. 297 (1986), no. 2, 645–650. MR 854090, DOI 10.1090/S0002-9947-1986-0854090-X
- Robert Finn, Remarks relevant to minimal surfaces, and to surfaces of prescribed mean curvature, J. Analyse Math. 14 (1965), 139–160. MR 188909, DOI 10.1007/BF02806384
- Thomas James Higgins, Analogic experimental methods in stress analysis as exemplified by Saint-Venant’s torsion problem, Experimental Stress Analysis 2 (1945), 17–27. MR 0012570 R. Gulliver, personal communication.
- Graham H. Williams, The Dirichlet problem for the minimal surface equation, Instructional Workshop on Analysis and Geometry, Part I (Canberra, 1995) Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 34, Austral. Nat. Univ., Canberra, 1996, pp. 91–110. MR 1394678
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 187-188
- MSC: Primary 35J60; Secondary 49F10, 53A10
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813836-2
- MathSciNet review: 813836