Premium
On Second‐Order Almost‐Periodic Elliptic Operators
Author(s) -
Dungey N.,
ter Elst A. F. M.,
Robinson Derek W.
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1017/s0024610701002149
Subject(s) - heat kernel , mathematics , elliptic operator , kernel (algebra) , homogenization (climate) , asymptotic expansion , order (exchange) , pure mathematics , gaussian , divergence (linguistics) , mathematical analysis , physics , economics , biology , biodiversity , ecology , linguistics , philosophy , finance , quantum mechanics
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 H ^ of H is the leading term in the asymptotic expansion of t ↦ K t .