Stochastic partial differential equations

Head:
Benjamin Gess (Email, Homepage)

Phone:
+49 (0) 341 - 9959 - 954

Fax:
+49 (0) 341 - 9959 - 585

Address:
Inselstr. 22
04103 Leipzig

Publications

Preprints

Becker, S. ; Gess, B. ; Jentzen, A. and P. E. Kloeden: Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. Bibtex [ARXIV]

Dareiotis, K. and B. Gess: Nonlinear diffusion equations with nonlinear gradient noise. Bibtex [ARXIV]

Fehrman, B. J. and B. Gess: Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise. Bibtex [ARXIV]

Gassiat, P. ; Gess, B. ; Lions, P. and P. E. Souganidis: Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. Bibtex [ARXIV]

Becker, S. ; Gess, B. ; Jentzen, A. and P. E. Kloeden: Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations. Bibtex [ARXIV]

Chouk, K. and B. Gess: Path-by-path regularization by noise for scalar conservation laws. Bibtex [ARXIV]

Fehrman, B. J. and B. Gess: Well-posedness of stochastic porous media equations with nonlinear, conservative noise. Bibtex [ARXIV]

Gess, B. : Sobolev regularity for the porous medium equation with a force. Bibtex [ARXIV]

Gess, B. ; Ouyang, C. and S. Tindel: Density bounds for solutions to differential equations driven by Gaussian rough paths. Bibtex [ARXIV]

Friz, P. K. ; Gess, B. ; Gulisashvili, A. and S. Riedel: Spatial rough path lifts of stochastic convolutions. Bibtex [ARXIV]

Friz, P. K. ; Gess, B. and S. Riedel: On the variational regularity of Cameron-Martin paths. Bibtex [ARXIV]

Publications

Dareiotis, K. ; Gerencscér, M. and B. Gess: Entropy solutions for stochastic porous media equations. Journal of differential equations, Vol. not yet known, pp. not yet known Bibtex [DOI][ARXIV]

Dareiotis, K. and B. Gess: Supremum estimates for degenerate, quasilinear stochastic partial differential equations. Annales de l'Institut Henri Poincaré / B, Vol. not yet known, pp. not yet known Bibtex [ARXIV]

Gassiat, P. and B. Gess: Regularization by noise for stochastic Hamilton-Jacobi equations. Probability theory and related fields, Vol. not yet known, pp. not yet known Bibtex [DOI][ARXIV]

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

Gess, B. and X. Lamy: Regularity of solutions to scalar conservation laws with a force. Annales de l'Institut Henri Poincaré / C, Vol. not yet known, pp. not yet known Bibtex [DOI][ARXIV]

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

Flandoli, F. ; Gess, B. and M. Scheutzow: Synchronization by noise for order-preserving random dynamical systems. The annals of probability, 45 (2017) 2, p. 1325-1350 Bibtex [DOI][ARXIV]

Gess, B. and M. Röckner: 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]

Gess, B. and S. A. Smith: Stochastic continuity equations with conservative noise. Journal de mathématiques pures et appliquées, Vol. not yet known, pp. not yet known Bibtex [ARXIV]

Gess, B. and P. E. Souganidis: 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]

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

Friz, P. K. and B. Gess: Stochastic scalar conservation laws driven by rough paths. Annales de l'Institut Henri Poincaré / C, 33 (2016) 4, p. 933-963 Bibtex [DOI][ARXIV]

Friz, P. K. ; Gess, B. ; Gulisashvili, A. and S. Riedel: 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]

Gassiat, P. and B. Gess: 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. and M. Maurelli: Well-posedness by noise for scalar conservation laws. Communications in partial differential equations, Vol. not yet known, pp. not yet known Bibtex [ARXIV]

Gess, B. ; Perthame, B. and P. E. Souganidis: 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]

Gess, B. and J. M. Tölle: 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]

Gess, B. and J. M. Tölle: Stability of solutions to stochastic partial differential equations. Journal of differential equations, 260 (2016) 6, p. 4973-5025 Bibtex [DOI][ARXIV]

Cranston, M. ; Gess, B. and M. Scheutzow: Weak synchronization for isotropic flows. Discrete and continuous dynamical systems / B, 21 (2015) 9, p. 3003-3014 Bibtex [DOI][ARXIV]

Gess, 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]

Gess, B. and M. Röckner: Singular-degenerate multivalued stochastic fast diffusion equations. SIAM journal on mathematical analysis, 47 (2015) 5, p. 4058-4090 Bibtex [DOI][ARXIV]

Gess, B. and P. E. Souganidis: Scalar conservation laws with multiple rough fluxes. Communications in mathematical sciences, 13 (2015) 6, p. 1569-1597 Bibtex [DOI][ARXIV]

Gess, 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]

Gess, B. and J. M. Tölle: Multi-valued, singular stochastic evolution inclusions. Journal de mathématiques pures et appliquées, 101 (2014) 6, p. 789-827 Bibtex [DOI][ARXIV]

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

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

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

Gess, 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]

Gess, B. : Strong solutions for stochastic partial differential equations of gradient type. Journal of functional analysis, 263 (2012) 8, p. 2355-2383 Bibtex [DOI][ARXIV]

Gess, B. ; Friz, P. K. ; Gulisashvili, A. and S. Riedel: 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 M. Röckner: 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]

Beyn, W. ; Gess, B. ; Lescot, P. and M. Röckner: 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]

Thesis

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

Gess, B. : Convexity of Chebyshev sets. Masterarbeit, Warwick University, 2009 Bibtex

16.12.2018, 05:30