Well-posedness of semilinear stochastic wave equations with Hölder continuous coefficients

We prove that semilinear stochastic abstract wave equations, including wave and plate equations, are well-posed in the strong sense with an $\alpha$-H\"older continuous drift coefficient, if $\alpha \in (2/3,1)$.
The uniqueness may fail for the corresponding
deterministic PDE and well-posedness is restored
by adding an external random forcing of
white noise type. This shows a
kind of regularization by noise
for the semilinear wave equation.
To prove the result we introduce an
approach based on backward stochastic differential equations.
We also establish regularizing properties of the transition semigroup associated to the
stochastic wave equation by using control theoretic results.