Skip to main content
3 of 3
added 23 characters in body
Francesco Polizzi
  • 66.3k
  • 5
  • 180
  • 283

Sobolev embedding for fractional Sobolev spaces

Let $\Omega\subset\mathbb{R}^2$ be open and of class $C^1$. The Sobolev embedding theorem implies that if $u\in W^{k,2}(\Omega)$ and if $k\in\mathbb{N}: k\geq 2$, then $u$ is continuous.

Question. Does there exist a similar result for fractional Sobolev Spaces? For example, if $u\in W^{1+\theta,2}(\Omega)$ for some $\theta\in (0,1)$, then can we say that $u$ is continuous?

Nirav
  • 347
  • 1
  • 11