Estimates for Nonlinear Stochastic Partial Differential Equations with Gradient Noise via Dirichlet Forms

  • Jonas M. TölleEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)


We present a priori estimates for nonlinear Stratonovich stochastic partial differential equations on the d-dimensional torus with p-Laplace-type drift with sublinear non-homogeneous nonlinearities and Gaussian gradient Stratonovich noise with \(C^{1}\)-vector field coefficients. Assuming a commutator bound, the results are obtained by using resolvent and Dirichlet form methods and an approximative Itô-formula.


Nonlinear stochastic partial differential equations Dirichlet forms A Priori estimate Stochastic p-laplace evolution equation Gradient Stratonovich noise Commutator bound Bakry-Émery curvature-dimension condition 

2010 Mathematics Subject Classification

35K55 35K92 60H15 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für MathematikUniversität AugsburgAugsburgGermany

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