Symplectic homology of disc cotangent bundles of domains in Euclidean space

Let $V$ be a bounded domain with smooth boundary in ${\mathbb{R}}^n$, and $D^{\ast }V$ denote its disc cotangent bundle. We compute symplectic homology of $D^{\ast }V$, in terms of relative homology of loop spaces on the closure of $V$. We use this result to show that Floer-Hofer capacity of $D^{\ast }V$ is between $2r(V)$ and $2(n+1)r(V)$, where $r(V)$ denotes inradius of $V$. As an application, we study periodic billiard trajectories on $V$.