The paper under consideration deals with a free boundary problem for compressible-incompressible two-phase flows with phase transitions in the isentropic case. Two immiscible viscous fluids are separated by a sharp interface with taken a surrface tension into account. One has to determine the subdomains occupied by the two fluids which are changing in time as well as the flow fields like \(\vec{v} \, \varrho\). The domains are contained in \(\mathbb{R}^{N}\), \(N \geq 2\), can be bounded or exterior domains in \(\mathbb{R}^{N}\). In the model of the author, the motion of the compressible fluid is described by Navier-Stokes-Korteweg equations while the incompessible one is described by the Navier-Stokes equations only. The main result of the paper consists in the proof that, for given \(T > 0\), the problem admits a unique strong solution on \((0,T)\) in the maximal \( L{p} - L_{q}\) regularity class provided that the initial data are small in their natural norms. The paper contains 20 well choosen references that give a good survey on the state of the art. Although the paper contains a lot of estimates including the application of various functional-analytic tools it reads sufficiently good. One is able to follow the most derivations of this article.