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elliptic evolution equation

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Decay rates at infinity for solutions to periodic Schrödinger equations
Part of
- Partial differential equations
- Elliptic equations and systems
Daniel M. Elton
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 3 / June 2020

Published online by Cambridge University Press:

30 January 2019, pp. 1113-1126

Print publication:

June 2020
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We consider the equation Δu = Vu in the half-space ${\open R}_ + ^d $, d ⩾ 2 where V has certain periodicity properties. In particular, we show that such equations cannot have non-trivial superexponentially decaying solutions. As an application this leads to a new proof for the absolute continuity of the spectrum of particular periodic Schrödinger operators. The equation Δu = Vu is studied as part of a broader class of elliptic evolution equations.