Pathwise uniqueness for stochastic reaction-diffusion equations in   Banach spaces with an H\"{o}lder drift component
  We prove pathwise uniqueness for an abstract stochastic reaction-diffusion equation in Banach spaces. The drift contains a bounded H\"{o}lder term; in spite of this, due to the space-time white noise it is possible to prove pathwise uniqueness. The proof is based on a detailed analysis of the associated Kolmogorov equation. The model includes examples not covered by the previous works based on Hilbert spaces or concrete SPDEs. 
Sandra Cerrai, Giuseppe Da Prato and Franco Flandoli
math.AP