Asymptotic Behaviour Of The Least Energy Solutions To Fractional Neumann Problems

We study the asymptotic behaviour of the least energy solutions to the following class of nonlocal Neumann problems: 0} \text{in } \Omega, \\ { \mathcal{N}_{s}u=0 } \text{in } \mathbb{R}^{n}\setminus \overline{\Omega}, \end{cases} \end{align*} $$ ]]> where is a bounded domain of class, <![CDATA[ $1<p\max \{1, 2s \}, 00$ ]] and is the nonlocal Neumann derivative. We show that for small the least energy solutions of the above problem achieve an-bound independent of Using this together with suitable-estimates on we show that the least energy solution achieves a maximum on the boundary of for d sufficiently small.