Phragmén-Lindelöf theorem for the minimal surface equation
HTML articles powered by AMS MathViewer
- by Jenn-Fang Hwang PDF
- Proc. Amer. Math. Soc. 104 (1988), 825-828 Request permission
Abstract:
It is proved that if $u$ satisfies the minimal surface equation in an unbounded domain $\Omega$ which is properly contained in a half plane, then the growth property of $u$ depends on $\Omega$ and the boundary value of $u$ only.References
- Patricio Aviles, Phragmén-Lindelöf and nonexistence theorems for nonlinear elliptic equations, Manuscripta Math. 43 (1983), no. 2-3, 107–129. MR 707041, DOI 10.1007/BF01165827
- Avner Friedman, On two theorems of Phragmén-Lindelöf for linear elliptic and parabolic differential equations of the second order, Pacific J. Math. 7 (1957), 1563–1575. MR 100713, DOI 10.2140/pjm.1957.7.1563
- Seppo Granlund, A Phragmén-Lindelöf principle for subsolutions of quasilinear equations, Manuscripta Math. 36 (1981/82), no. 3, 355–365. MR 641981, DOI 10.1007/BF01322498
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR 0473443, DOI 10.1007/978-3-642-96379-7
- David Gilbarg, The Phragmén-Lindelöf theorem for elliptic partial differential equations, J. Rational Mech. Anal. 1 (1952), 411–417. MR 50122, DOI 10.1512/iumj.1952.1.51011
- Eberhard Hopf, Remarks on the preceding paper by D. Gilbarg, J. Rational Mech. Anal. 1 (1952), 419–424. MR 50123, DOI 10.1512/iumj.1952.1.51012
- Keith Miller, Extremal barriers on cones with Phragmén-Lindelöf theorems and other applications, Ann. Mat. Pura Appl. (4) 90 (1971), 297–329. MR 316884, DOI 10.1007/BF02415053
- Johannes C. C. Nitsche, On new results in the theory of minimal surfaces, Bull. Amer. Math. Soc. 71 (1965), 195–270. MR 173993, DOI 10.1090/S0002-9904-1965-11276-9 —, Vorlesungen über Minimalflächen, Springer-Verlag, Berlin-Heidelberg-New York, 1975.
- A. A. Novruzov, Theorems of Phragmén-Lindelöf type for solutions of second-order linear and quasilinear elliptic equations with discontinuous coefficients, Dokl. Akad. Nauk SSSR 266 (1982), no. 3, 549–552 (Russian). MR 672381
- Robert Osserman, A survey of minimal surfaces, Van Nostrand Reinhold Co., New York-London-Melbourne, 1969. MR 0256278
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
- J. B. Serrin, On the Phragmén-Lindelöf principle for elliptic differential equations, J. Rational Mech. Anal. 3 (1954), 395–413. MR 62918, DOI 10.1512/iumj.1954.3.53020
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 825-828
- MSC: Primary 35B05; Secondary 35J60, 49F10, 53A10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0964864-X
- MathSciNet review: 964864