Um estudo dos espaços de Sobolev fracionários e aplicação a uma classe de equações elípticas - Alencar, Ozana Da Silva (2019)
In this work, we study the fractional Sobolev spaces Ws;p() which are de ned through Gagliardo's seminorm when s 2 (0; 1). In the particular case where p = 2 we take a Fourier transform approach. Then we can relate the space Hs(Rn) = Ws;2(Rn) with the fractional Laplacian operator. Finally, we seek a solution to an elliptic partial di erential equation involving the fractional Laplacian operator