| Abstract: |
| Nelson Dunford and Billy James Pettis [{\em Trans. Amer. Math. Soc.}, 47 (1940), pp. 323--392] proved that relatively weakly compact subsets of $ L^1 $ coincide with equi-integrable families. We expand it to the case of $ W^{k,1} $ - the non-reflexive Sobolev spaces - by a tailor-made isometric operator. Herein we extend an existence theorem of minimizers from reflexive Sobolev spaces to non-reflexive ones. |
|