7
votes
2answers
707 views

Extension theory with bump function

Let $B_t(0)$ denote the $n$ dimensional ball of radius $t$ centered at the origin. Does there exist a $\phi\in C(\mathbb{R}^n)$ function with the properties: $ \phi (x) = \begin{cases} 1&x\in ...
1
vote
1answer
656 views

Sobolev-Slobodeckij spaces for p=infinity

For $1\leq p<\infty$ an approach to define fractional Sobolev spaces is by Sobolev-Slobodeckij spaces a generalisation of Hölder continuity. For example letting $U\subset\mathbb{R}^n$ then, $ ...