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arXiv · 1910.01816

An order approach to SPDEs with antimonotone terms

Luca Scarpa·Ulisse Stefanelli
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Abstract

We consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions is proved via a fixed-point argument for nondecreasing mappings in ordered spaces. This relies on the validity of a comparison principle.

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Luca Scarpa, Ulisse Stefanelli. 2019-10-04. An order approach to SPDEs with antimonotone terms. https://doi.org/10.1007/s40072-019-00161-7

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