Harnack inequality for the linearized parabolic Monge-Ampere equation

Authors
Citation
Qb. Huang, Harnack inequality for the linearized parabolic Monge-Ampere equation, T AM MATH S, 351(5), 1999, pp. 2025-2054
Citations number
14
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
351
Issue
5
Year of publication
1999
Pages
2025 - 2054
Database
ISI
SICI code
0002-9947(199905)351:5<2025:HIFTLP>2.0.ZU;2-A
Abstract
In this paper we prove the Harnack inequality for nonnegative solutions of the linearized parabolic Monge-Ampere equation u(t) - tr((D(2)phi(x))(-1) D(2)u) = 0 on parabolic sections associated with phi(x), under the assumption that the Monge-Ampere measure generated by phi satisfies the doubling condition on sections and the uniform continuity condition with respect to Lebesgue meas ure. The theory established is invariant under the group AT(n) x AT(1), whe re AT(n) denotes the group of all invertible affine transformations on R-n.