On second-order almost-periodic elliptic operators

N. Dungey; A. F.M. Ter Elst; Derek W. Robinson

doi:10.1017/S0024610701002149

On second-order almost-periodic elliptic operators

N. Dungey^*, A. F.M. Ter Elst, Derek W. Robinson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The paper considers second-order, strongly elliptic, operators H with complex almost-periodic coefficients in divergence form on R^d. 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 Ĥ of H is the leading term in the asymptotic expansion of t→K_t.

Original language	English
Pages (from-to)	735-753
Number of pages	19
Journal	Journal of the London Mathematical Society
Volume	63
Issue number	3
DOIs	https://doi.org/10.1017/S0024610701002149
Publication status	Published - Jun 2001

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10.1017/S0024610701002149

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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 H{\"o}lder continuous and Gaussian bounds are derived with the correct small and large time asymptotic behaviour on the kernel and its H{\"o}lder 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 Ĥ of H is the leading term in the asymptotic expansion of t→Kt.",

author = "N. Dungey and {Ter Elst}, {A. F.M.} and Robinson, {Derek W.}",

year = "2001",

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AU - Dungey, N.

AU - Ter Elst, A. F.M.

AU - Robinson, Derek W.

PY - 2001/6

Y1 - 2001/6

N2 - 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 Ĥ of H is the leading term in the asymptotic expansion of t→Kt.

AB - 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 Ĥ of H is the leading term in the asymptotic expansion of t→Kt.

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DO - 10.1017/S0024610701002149

M3 - Article

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VL - 63

SP - 735

EP - 753

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -

On second-order almost-periodic elliptic operators

Abstract

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