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stochastic partial differential equations 2additive noise 1error analysis 1finite element method 1local Lipschitz conditions 1nonsmooth initial data 1rough initial data 1semilinear SPDEs 1well-posedness 1

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math.AP2026

Existence, Uniqueness, and Pathwise Regularity for Multidimensional Semilinear SPDEs with Locally Lipschitz Coefficients and Rough Initial Data

Jitendra Nath Naik, Lok Pati Tripathi

The paper proves existence, uniqueness, and pathwise regularity for multidimensional semilinear stochastic PDEs with multiplicative noise, allowing locally Lipschitz coefficients a…