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arXiv · 1212.5377

Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an Hölder drift component

Sandra Cerrai·Giuseppe Da Prato·Franco Flandoli
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Abstract

We prove pathwise uniqueness for an abstract stochastic reaction-diffusion equation in Banach spaces. The drift contains a bounded Hölder 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.

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Sandra Cerrai, Giuseppe Da Prato, Franco Flandoli. 2012-12-21. Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an Hölder drift component. https://arxiv.org/abs/1212.5377

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