Abstract
We prove Liouville-type theorems for solutions of linear homogeneous elliptic systems of partial differential equations, with variable coefficients and of arbitrary order. We require certain growth and smoothness conditions on the coefficients, and coerciveness and ellipticity condtions on the differential operators. Under various hypotheses it is established that solutions defined in all of Euclidean space, of a prescribed growth or decay at infinity, are necessarily constant, identically zero, or polynomials
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.