Phragmén-Lindelöf theorem for the minimal surface equation

Hwang, Jenn-Fang

doi:10.1090/S0002-9939-1988-0964864-X

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

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