On second-order almost-periodic elliptic operators

N. Dungey, A.F.M. Elst, ter, D.W. Robinson

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

The paper considers second-order, strongly elliptic, operators H with complex almost-periodic coefficients in divergence form on Rd. First, it is proved that the corresponding heat kernel is Hölder continuous and Gaussian bounds are derived with the correct small and large time asymptotic behaviour on the kernel and its Hölder derivatives. Secondly, it is established that the kernel has a variety of properties of almost-periodicity. Thirdly, it is demonstrated that the kernel of the homogenization of H is the leading term in the asymptotic expansion of t ¿ Kt.
Original languageEnglish
Pages (from-to)735-753
JournalJournal of the London Mathematical Society. Second Series
Volume63
Issue number3
DOIs
Publication statusPublished - 2001

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