Publications and Research
Document Type
Article
Publication Date
2016
Abstract
We obtain Liouville-type results for closed and p-pseudo-coclosed differential 1-forms ! with energy of lim inf r!1 1 r2 R B(x0;r) j!jqdv < 1 (that is, 2-finite growth), which extends finite q-energy ( R M j!jqdv < 1) in Lq spaces to infinite q-energy ( R M j!jqdv = 1) in non-Lq spaces. In particular, we recapture mathematicians' vanishing results of Liouville- type theorem for ! with finite q-energy in Lq spaces. Our method in this paper provides a successful way to work on Liouville-type problems for differential forms with a variety of energy conditions in broad spaces.
Comments
This article was originally published in the International Journal of Mathematical Analysis, available at https://doi.org/10.12988/ijma.2016.610117.
This article is distributed under the Creative Commons Attribution License.