Journal article
THE EXPONENTIAL GROWTH AND DECAY PROPERTIES FOR SOLUTIONS TO ELLIPTIC EQUATIONS IN UNBOUNDED CYLINDERS
Journal of the Korean Mathematical Society, Vol.57(6), pp.1573-1590
11/01/2020
DOI: 10.4134/JKMS.j190836
Abstract
In this paper, we classify all solutions bounded from below to uniformly elliptic equations of second order in the form of Lu(x) = a(ij)(x)D(ij)u(x) + b(i)(x)D(i)u(x) + c(x)u(x) = f (x) or Lu(x) = D-i(a(ij)D(j)u(x)) + b(i)(x)D(i)u(x) + c(x)u(x) = f (x) in unbounded cylinders. After establishing that the Aleksandrov maximum principle and boundary Harnack inequality hold for bounded solutions, we show that all solutions bounded from below are linear combinations of solutions, which are sums of two special solutions that exponential growth at one end and exponential decay at the another end, and a bounded solution that corresponds to the inhomogeneous term f of the equation.
Details
- Title: Subtitle
- THE EXPONENTIAL GROWTH AND DECAY PROPERTIES FOR SOLUTIONS TO ELLIPTIC EQUATIONS IN UNBOUNDED CYLINDERS
- Creators
- Lidan Wang - Shanghai Jiao Tong UniversityLihe Wang - Shanghai Jiao Tong UniversityChunqin Zhou - Max Planck Society
- Resource Type
- Journal article
- Publication Details
- Journal of the Korean Mathematical Society, Vol.57(6), pp.1573-1590
- Publisher
- KOREAN MATHEMATICAL SOC
- DOI
- 10.4134/JKMS.j190836
- ISSN
- 0304-9914
- eISSN
- 2234-3008
- Number of pages
- 18
- Grant note
- 11771285 / NSFC of China
- Language
- English
- Date published
- 11/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984241159602771
Metrics
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