# classical solution of fractional laplacian

What is meant by a classical solution of a fractional laplacian in $(-\Delta)^su= f(u)\text{ in } \mathbb{R}^N$ with no condition at infinity. If one can show that u is a weak solution of the above solution, how do one show it is classical.

• I would guess that "classical" means "pointwise"; I am not sure what would "no condition at infinity" mean. Can you provide a broader context? Mar 22 '18 at 10:16
• I thought any bounded weak solution is a classical solution (smooth in space and time) Mar 22 '18 at 11:15
• By "no condition at infinity", the solution may be bounded or does not decay at infinity. Mar 23 '18 at 15:55