A three-curves theorem for viscosity subsolutions of parabolic equations
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- by Jay Kovats
- Proc. Amer. Math. Soc. 131 (2003), 1509-1514
- DOI: https://doi.org/10.1090/S0002-9939-02-06664-9
- Published electronically: September 4, 2002
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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
- 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, DOI 10.1090/coll/043
- 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.
- E. M. Landis, A three-spheres theorem, Dokl. Akad. Nauk SSSR 148 (1963), 277–279 (Russian). MR 0150445
- Keith Miller, Three circle theorems in partial differential equations and applications to improperly posed problems, Arch. Rational Mech. Anal. 16 (1964), 126–154. MR 164136, DOI 10.1007/BF00281335
- 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, DOI 10.1007/978-1-4612-5282-5
- Lihe Wang, On the regularity theory of fully nonlinear parabolic equations. I, Comm. Pure Appl. Math. 45 (1992), no. 1, 27–76. MR 1135923, DOI 10.1002/cpa.3160450103
Bibliographic Information
- Jay Kovats
- Affiliation: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901
- MR Author ID: 635359
- Email: jkovats@zach.fit.edu
- Received by editor(s): December 15, 2001
- Published electronically: September 4, 2002
- Communicated by: David S. Tartakoff
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1509-1514
- MSC (2000): Primary 35B05, 35K55
- DOI: https://doi.org/10.1090/S0002-9939-02-06664-9
- MathSciNet review: 1949881