• Corpus ID: 248495993

Extremal functions for the second-order Sobolev inequality on groups of polynomial growth

  title={Extremal functions for the second-order Sobolev inequality on groups of polynomial growth},
  author={Bobo Hua and Ruo Li and Florentin M{\"u}nch},
. In this paper, we prove the second-order Sobolev inequalities on Cayley graphs of groups of polynomial growth. We use the discrete Concentration- Compactness principle to prove the existence of extremal functions for best constants in supercritical cases. As applications, we get the existence of posi- tive ground state solutions to the p -biharmonic equations and the Lane-Emden systems. 

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