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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.


This article was originally published in the International Journal of Mathematical Analysis, available at

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