Bulletin of the
Korean Mathematical Society BKMS

Let $(G,v)$ be a bounded smooth domain and reflection vector field on $\partial G$, which points uniformly into $G$. Under the condition that locally for some coordinate system, $|v^i|< cv^d$, $i=1 ,\cdot , \cdot , d-1$, where $c$ is a constant depending on the Lipschitz constant of G, we have tightness for reflected diffusion with jump on $G$ with reflection $v$ depending only on $c$. From this, we obtain some properties of L-harmonic function where L is a sum of Laplacian and integro one.

Keywords: reflected diffusion, Lipschitz domain, oblique reflection

MSC numbers: 60J60