For 10 points, identify this French mathematician, who names that inequality with Schwarz.
For initial value problems, he names a boundary condition that is a weighted mean of the Dirichlet and Neumann conditions, and he names the existence and uniqueness theorem for analytical PDEs with Kowalevski. He lends his name to some equations that provide a necessary and sufficient condition for a  differentiable function to be (*) holomorphic in an open set with Riemann. On an inner product space, the absolute value of the inner product of x and y is less than or equal to the norm of x times the norm of y in a statement attributed to him and a German. For 10 points, identify this French mathematician, who names that inequality with Schwarz.
For initial value problems, he names a boundary condition that is a weighted mean of the Dirichlet and Neumann conditions, and he names the existence and uniqueness theorem for analytical PDEs with Kowalevski.
Agustin Louis {Cauchy}