Harnack inequality for the linearized parabolic MongeAmpère equation
Author:
Qingbo Huang
Journal:
Trans. Amer. Math. Soc. 351 (1999), 20252054
MSC (1991):
Primary 35K10; Secondary 35B45
Published electronically:
January 27, 1999
MathSciNet review:
1467468
Fulltext PDF Free Access
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Abstract: In this paper we prove the Harnack inequality for nonnegative solutions of the linearized parabolic MongeAmpère equation on parabolic sections associated with , under the assumption that the MongeAmpère measure generated by satisfies the doubling condition on sections and the uniform continuity condition with respect to Lebesgue measure. The theory established is invariant under the group , where denotes the group of all invertible affine transformations on .
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 D. Gilbarg & N. S. Trudinger, Elliptic partial differential equations of second order, 2nd edition, SpringerVerlag, 1983. MR 86c:35035
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 C. E. Gutiérrez, On the Harnack inequality for viscosity solutions of nondivergence equations, preprint.
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 C. E. Gutiérrez & Q. Huang, Geometric properties of the sections of solutions of the MongeAmpère equation, Trans. AMS. to appear.
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 N. V. Krylov & M. V. Safonov, Certain properties of solutions of parabolic equations with measurable coefficients, Izvestia Akad. Nauk. SSSR 44 (1980), 161175. MR 83c:35059
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 K. S. Tso, On an AlekandrovBakel'man type maximum principle for secondorder parabolic equations, Comm. PDE 10 (1985), 543553. MR 87f:35031
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Additional Information
Qingbo Huang
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Address at time of publication:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email:
qhuang@math.utexas.edu
DOI:
http://dx.doi.org/10.1090/S000299479902142X
PII:
S 00029947(99)02142X
Keywords:
Harnack inequality,
affine invariant,
linear parabolic MongeAmp\`{e}re equation,
section
Received by editor(s):
December 15, 1996
Received by editor(s) in revised form:
May 13, 1997
Published electronically:
January 27, 1999
Article copyright:
© Copyright 1999
American Mathematical Society
