Strong Solutions for Stochastic Partial Differential Equations of Gradient Type
By Benjamin Gess. 2011
81 citations recorded by the source corpus.
Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a genuinely new method of weighted Galerkin approximations based on the "distance" defined by the quasi-convex function. Spatial regularization of the initial condition analogous to the deterministic case is obtained. The results yield a unified framework which is applied to stochastic generalized porous media equations, stochastic generalized reaction diffusion equations and stochastic generalized degenerated p-Laplace equations. In particular, higher regularity for solutions of such SPDE is obtained.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/61fe77dffafae219e27a36678bb51886e74ab8c7
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In Computational Theory and Mathematics
- Tusheng Zhang
- Wei Liu
- Michael Röckner
- Shijie Shang
- Xicheng Zhang
- Feng-Yu Wang
- Wei David Liu
- Giuseppe Da Prato
In Control and Systems Engineering
- Wei Liu
- Tusheng Zhang
- Shijie Shang
- Michael Röckner
- Xicheng Zhang
- Franco Flandoli
- Wei David Liu
- Giuseppe Da Prato
In Finance
- Tusheng Zhang
- Wei Liu
- Michael Röckner
- Shijie Shang
- Xicheng Zhang
- Feng-Yu Wang
- A. Budhiraja
- Paul Dupuis
Citations in the corpus
- Well-posedness of stochastic partial differential equations with Lyapunov condition (2013, methodology): “2) has been established in [21] for a class of SPDE with additive noise using some Yosida approximation techniques (see also [11,30]).”
- Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, methodology): “see [48, 27, 5] for regularity of solutions, [18, 74, 47, 19, 88, 52, 61, 87, 37, 38] for large deviation principle, [31, 32, 33, 78, 65, 4, 90] for numerical approximation, [84, 46, 85, 86] for the Harnack inequality, gradient estimates, invariant measure and ergodicity, [28, 29] for random attract”