# Publications

## Preprints

Dareiotis, K.
; Gerencscér, M.
and Gess, B.
:

*Porous media equations with multiplicative space-time white noise*. Bibtex [ARXIV] Repository Open AccessFehrman, B.
J. and Gess, B.
:

*Large deviations for conservative stochastic PDE and non-equilibrium fluctuations*. Bibtex [ARXIV] Repository Open AccessGess, B.
; Sauer, J.
and Tadmor, E.
:

*Optimal regularity in time and space for the porous medium equation*. (Analysis and PDE) Bibtex [ARXIV] Repository Open AccessFehrman, B.
J. and Gess, B.
:

*Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise*. Bibtex [ARXIV] Repository Open AccessBecker, S.
; Gess, B.
; Jentzen, A.
and Kloeden, P.
E.:

*Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations*. Bibtex [ARXIV] Repository Open AccessGess, B.
:

*Optimal regularity for the porous medium equation*. (Journal of the European Mathematical Society) Bibtex [ARXIV] Repository Open AccessFriz, P.
K. ; Gess, B.
; Gulisashvili, A.
and Riedel, S.
:

*Spatial rough path lifts of stochastic convolutions*. Bibtex [ARXIV] Repository Open AccessFriz, P.
K. ; Gess, B.
and Riedel, S.
:

*On the variational regularity of Cameron-Martin paths*. Bibtex [ARXIV] Repository Open Access## Publications

Becker, S.
; Gess, B.
; Jentzen, A.
and Kloeden, P.
E.:

*Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations*. BIT : numerical mathematics, Vol. not yet known, pp. not yet known Bibtex [DOI] [ARXIV] Repository Open AccessDareiotis, K.
and Gess, B.
:

*Nonlinear diffusion equations with nonlinear gradient noise*. Electronic journal of probability, 25 (2020), 35 Bibtex [DOI] [ARXIV] Journal Open AccessDareiotis, K.
; Gess, B.
and Tsatsoulis, P.
:

*Ergodicity for stochastic porous media equations with multiplicative noise*. SIAM journal on mathematical analysis, 52 (2020) 5, p. 4524-4564 Bibtex [DOI] [ARXIV] Repository Open AccessFehrman, B.
J. ; Gess, B.
and Jentzen, A.
:

*Convergence rates for the stochastic gradient descent method for non-convex objective functions*. Journal of machine learning research, 21 (2020) 136, p. 1-48 Bibtex [ARXIV] [FREELINK] Journal Open AccessGassiat, P.
; Gess, B.
; Lions, P.
and Souganidis, P.
E.:

*Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians*. Probability theory and related fields, 176 (2020) 1/2, p. 421-448 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Gnann, M.
V.:

*The stochastic thin-film equation : existence of nonnegative martingale solutions*. Stochastic processes and their applications, 130 (2020) 12, p. 7260-7302 Bibtex [DOI] [ARXIV] [FREELINK] Repository Open AccessGess, B.
; Liu, W.
and Schenke, A.
:

*Random attractors for locally monotone stochastic partial differential equations*. Journal of differential equations, 269 (2020) 4, p. 3414-3455 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
; Ouyang, C.
and Tindel, S.
:

*Density bounds for solutions to differential equations driven by Gaussian rough paths*. Journal of theoretical probability, 33 (2020) 2, p. 611-648 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Tsatsoulis, P.
:

*Synchronization by noise for the stochastic quantization equation in dimensions \(2\) and \(3\)*. Stochastics and dynamics, 20 (2020) 6, 240006 Bibtex [DOI] [ARXIV] Repository Open AccessChouk, K.
and Gess, B.
:

*Path-by-path regularization by noise for scalar conservation laws*. Journal of functional analysis, 277 (2019) 5, p. 1469-1498 Bibtex [DOI] [ARXIV] Repository Open AccessCoghi, M.
and Gess, B.
:

*Stochastic nonlinear Fokker-Planck equations*. Nonlinear analysis / A, 187 (2019), p. 259-278 Bibtex [DOI] [ARXIV] Repository Open AccessDareiotis, K.
; Gerencscér, M.
and Gess, B.
:

*Entropy solutions for stochastic porous media equations*. Journal of differential equations, 266 (2019) 6, p. 3732-3763 Bibtex [DOI] [ARXIV] Repository Open AccessDareiotis, K.
and Gess, B.
:

*Supremum estimates for degenerate, quasilinear stochastic partial differential equations*. Annales de l'Institut Henri Poincaré / B, 55 (2019) 3, p. 1765-1796 Bibtex [DOI] [ARXIV] Journal Open AccessFehrman, B.
J. and Gess, B.
:

*Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise*. Archive for rational mechanics and analysis, 233 (2019) 1, p. 249-322 Bibtex [DOI] [ARXIV] Journal Open AccessGassiat, P.
and Gess, B.
:

*Regularization by noise for stochastic Hamilton-Jacobi equations*. Probability theory and related fields, 173 (2019) 3/4, p. 1063-1098 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Lamy, X.
:

*Regularity of solutions to scalar conservation laws with a force*. Annales de l'Institut Henri Poincaré / C, 36 (2019) 2, p. 505-521 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Smith, S.
A.:

*Stochastic continuity equations with conservative noise*. Journal de mathématiques pures et appliquées, 128 (2019), p. 225-263 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
:

*Regularization and well-posedness by noise for ordinary and partial differential equations*. Stochastic partial differential equations and related fields : in honor of Michael Röckner, SPDERF, Bielefeld, Germany, October 10-14, 2016 / A. Eberle... (eds.). Springer, 2018. - P. 43-67 (Springer proceedings in mathematics and statistics ; 229) Bibtex [DOI] [FREELINK]Gess, B.
and Hofmanová, M.
:

*Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE*. The annals of probability, 46 (2018) 5, p. 2495-2544 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Maurelli, M.
:

*Well-posedness by noise for scalar conservation laws*. Communications in partial differential equations, 43 (2018) 12, p. 1702-1736 Bibtex [DOI] [ARXIV] Repository Open AccessFlandoli, F.
; Gess, B.
and Scheutzow, M.
:

*Synchronization by noise*. Probability theory and related fields, 168 (2017) 3/4, p. 511-556 Bibtex [DOI] [ARXIV] Repository Open AccessFlandoli, F.
; Gess, B.
and Scheutzow, M.
:

*Synchronization by noise for order-preserving random dynamical systems*. The annals of probability, 45 (2017) 2, p. 1325-1350 Bibtex [DOI] [ARXIV] Journal Open AccessGess, B.
and Röckner, M.
:

*Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations*. Transactions of the American Mathematical Society, 369 (2017) 5, p. 3017-3045 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Souganidis, P.
E.:

*Long-time behavior, invariant measures and regularizing effects for stochastic scalar conservation laws*. Communications on pure and applied mathematics, 70 (2017) 8, p. 1562-1597 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Souganidis, P.
E.:

*Stochastic non-isotropic degenerate parabolic-hyperbolic equations*. Stochastic processes and their applications, 127 (2017) 9, p. 2961-3004 Bibtex [DOI] [ARXIV] Repository Open AccessFriz, P.
K. and Gess, B.
:

*Stochastic scalar conservation laws driven by rough paths*. Annales de l'Institut Henri Poincaré / C, 33 (2016) 4, p. 933-963 Bibtex [DOI] [ARXIV] Repository Open AccessFriz, P.
K. ; Gess, B.
; Gulisashvili, A.
and Riedel, S.
:

*The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory*. The annals of probability, 44 (2016) 1, p. 684-738 Bibtex [DOI] [ARXIV] Repository Open AccessGassiat, P.
and Gess, B.
:

*Regularization by noise for stochastic Hamilton-Jacobi equations [In: Rough paths, regularity structures and related topics : 1 May - 7 May 2016 ; report no. 24/2016]*. Oberwolfach reports, 13 (2016) 2, p. 1349-1353 Bibtex [DOI]Gess, B.
; Perthame, B.
and Souganidis, P.
E.:

*Semi-discretization for stochastic scalar conservation laws with multiple rough fluxes*. SIAM journal on numerical analysis, 54 (2016) 4, p. 2187-2209 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Tölle, J.
M.:

*Ergodicity and local limits for stochastic local and nonlocal \(p\)-Laplace equations*. SIAM journal on mathematical analysis, 48 (2016) 6, p. 4094-4125 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Tölle, J.
M.:

*Stability of solutions to stochastic partial differential equations*. Journal of differential equations, 260 (2016) 6, p. 4973-5025 Bibtex [DOI] [ARXIV] Repository Open AccessCranston, M.
; Gess, B.
and Scheutzow, M.
:

*Weak synchronization for isotropic flows*. Discrete and continuous dynamical systems / B, 21 (2015) 9, p. 3003-3014 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
:

*Finite time extinction for stochastic sign fast diffusion and self-organized criticality*. Communications in mathematical physics, 335 (2015) 1, p. 309-344 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Röckner, M.
:

*Singular-degenerate multivalued stochastic fast diffusion equations*. SIAM journal on mathematical analysis, 47 (2015) 5, p. 4058-4090 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Souganidis, P.
E.:

*Scalar conservation laws with multiple rough fluxes*. Communications in mathematical sciences, 13 (2015) 6, p. 1569-1597 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
:

*Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise*. The annals of probability, 42 (2014) 2, p. 818-864 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
and Tölle, J.
M.:

*Multi-valued, singular stochastic evolution inclusions*. Journal de mathématiques pures et appliquées, 101 (2014) 6, p. 789-827 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
:

*Finite speed of propagation for stochastic porous media equation*. SIAM journal on mathematical analysis, 45 (2013) 5, p. 2734-2766 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
:

*Random attractors for singular stochastic evolution equations*. Journal of differential equations, 255 (2013) 3, p. 524-559 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
:

*Random attractors for degenerate stochastic partial differential equations*. Journal of dynamics and differential equations, 25 (2013) 1, p. 121-157 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
:

*Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise*. Comptes rendus mathematique, 350 (2012) 5-6, p. 299-302 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
:

*Strong solutions for stochastic partial differential equations of gradient type*. Journal of functional analysis, 263 (2012) 8, p. 2355-2383 Bibtex [DOI] [ARXIV] Repository Open AccessGess, B.
; Friz, P.
K. ; Gulisashvili, A.
and Riedel, S.
:

*Spatial rough path lifts of stochastic convolutions [In: Rough paths and PDEs ; August 19-25th 2012 ; report no. 41/2012]*. Oberwolfach reports, 9 (2012) 3, p. 2509-2513 Bibtex [DOI]Gess, B.
; Liu, W.
and Röckner, M.
:

*Random attractors for a class of stochastic partial differential equations driven by general additive noise*. Journal of differential equations, 251 (2011) 4-5, p. 1225-1253 Bibtex [DOI] [ARXIV] Repository Open AccessBeyn, W.
; Gess, B.
; Lescot, P.
and Röckner, M.
:

*The global random attractor for a class of stochastic porous media equations*. Communications in partial differential equations, 36 (2010) 3, p. 446-469 Bibtex [DOI] [ARXIV] Repository Open Access## Thesis

Gess, B.
:

*Stochastic flows induced by stochastic partial differential equations*. Dissertation, Universität Bielefeld, 2011 BibtexGess, B.
:

*Convexity of Chebyshev sets*. Masterarbeit, Warwick University, 2009 Bibtex