Strichartz estimates for mixed homogeneous surfaces in three dimensions

We obtain sharp mixed norm Strichartz estimates associated to mixed homogeneous surfaces in $\mathbb{R}^3$. Both cases with and without a damping factor are considered. In the case when a damping factor is considered our results yield a wide generalization of a result of Carbery, Kenig, and Ziesler [CKZ13]. The approach we use is to first classify all possible singularities locally, after which one can tackle the problem by appropriately modifying the methods from the paper of Ginibre and Velo [GV92], and by using the recently developed methods by Ikromov and M\"uller [IM16].