Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A three-curves theorem for viscosity subsolutions of parabolic equations


Author: Jay Kovats
Journal: Proc. Amer. Math. Soc. 131 (2003), 1509-1514
MSC (2000): Primary 35B05, 35K55
Published electronically: September 4, 2002
MathSciNet review: 1949881
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a three-curves theorem for viscosity subsolutions of fully nonlinear uniformly parabolic equations $F(D^{2}u,t,x)-u_{t}=0$.


References [Enhancements On Off] (What's this?)

  • [CC] Luis A. Caffarelli and Xavier Cabré, Fully nonlinear elliptic equations, American Mathematical Society Colloquium Publications, vol. 43, American Mathematical Society, Providence, RI, 1995. MR 1351007
  • [G] R.J. Glagelova, The three-cylinder theorem and its applications, vol. 6, Dokl. Akad. Nauka S.S.S.R, Moscow, 1965, pp. 1004-1008, Translated in Soviet Math.
  • [L] E. M. Landis, A three-spheres theorem, Dokl. Akad. Nauk SSSR 148 (1963), 277–279 (Russian). MR 0150445
  • [M] Keith Miller, Three circle theorems in partial differential equations and applications to improperly posed problems, Arch. Rational Mech. Anal. 16 (1964), 126–154. MR 0164136
  • [PW] Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984. Corrected reprint of the 1967 original. MR 762825
  • [W] Lihe Wang, On the regularity theory of fully nonlinear parabolic equations. I, Comm. Pure Appl. Math. 45 (1992), no. 1, 27–76. MR 1135923, 10.1002/cpa.3160450103

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35B05, 35K55

Retrieve articles in all journals with MSC (2000): 35B05, 35K55


Additional Information

Jay Kovats
Affiliation: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901
Email: jkovats@zach.fit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06664-9
Received by editor(s): December 15, 2001
Published electronically: September 4, 2002
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society