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Multilevel Monte Carlo methods for the Dean-Kawasaki equation from fluctuating hydrodynamics,
together with Federico Cornalba,
submitted, 20 p., 2023.
arXiv:2311.08872 |
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Approximation of classical two-phase flows of viscous incompressible fluids by a Navier-Stokes/Allen-Cahn system,
together with Helmut Abels and Maximilian Moser,
submitted, 39 p., 2023.
arXiv:2311.02997 |
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Density fluctuations in weakly interacting particle systems via the Dean-Kawasaki equation,
together with Federico Cornalba, Jonas Ingmanns, and Claudia Raithel,
submitted, 73 p., 2023.
arXiv:2303.00429 |
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Local minimizers of the interface length functional based on a concept of local paired calibrations,
together with Sebastian Hensel, Tim Laux, and Theresa Simon,
submitted, 35 p., 2023.
arXiv:2212.11840 |
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A monotonicity formula for minimizers of the Mumford-Shah functional in 2d and a sharp lower bound on the energy density,
submitted, 16 p., 2022.
arXiv:2203.13177 |
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The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions,
together with Sebastian Hensel, Tim Laux, and Theresa Simon,
first part in (minor) revision at J. Eur. Math. Soc. (JEMS), 2023.
arXiv:2003.05478 |
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Quantitative normal approximation for sums of random variables with multilevel local dependence structure,
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Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow,
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to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire, 53 p., 2023.
arXiv:2203.17143 |
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The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles,
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Arch. Ration. Mech. Anal., 247:76, 2023.
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External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development,
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J. Convex Anal., 30(1):217-247, 2023. |
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Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion,
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J. Nonlinear Sci., 33:66, 2023.
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Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation,
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Comm. Partial Differential Equations, 47(7):1394-1434, 2022.
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Global existence analysis of energy-reaction-diffusion systems,
together with Katharina Hopf, Michael Kniely, and Alexander Mielke
SIAM J. Math. Anal., 54(1):220-267, 2022.
doi:10.1137/20M1387237 |
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Scaling limit of the homogenization commutator for Gaussian coefficient fields,
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Ann. Appl. Probab., 32(2):1179-1209, 2022. |
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Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,
together with Stefan Neukamm,
Arch. Ration. Mech. Anal., 242(1):343-452, 2021.
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A priori error analysis of a numerical stochastic homogenization method,
together with Dietmar Gallistl and Daniel Peterseim,
SIAM J. Numer. Anal. 59(2):660-674, 2021.
doi:10.1137/19M1308992 |
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The waiting time phenomenon in spatially discretized porous medium and thin film equations,
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SIAM J. Numer. Anal. 59(1):60-87, 2021.
doi:10.1137/19M1300017 |
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Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies,
together with Tim Laux and Theresa Simon,
SIAM J. Math. Anal. 52(6):6222-6233, 2020.
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Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,
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Nonlinearity 33:5733, 2020.
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Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension,
together with Sebastian Hensel,
Arch. Ration. Mech. Anal. 36(2):967-1087, 2020.
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The choice of representative volumes in the approximation of effective properties of random materials,
Arch. Ration. Mech. Anal. 234(2):635-726, 2019.
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Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with Lp data,
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J. Differential Equations 266:257-311, 2019.
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Existence of nonnegative solutions to stochastic thin-film equations,
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SIAM J. Math. Anal. 50(1):411-455, 2018.
doi:10.1137/16M1098796 |
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Stochastic homogenization of linear elliptic equations: Higher-order error estimates in weak norms via second-order correctors,
together with Peter Bella, Benjamin Fehrman, and Felix Otto,
SIAM J. Math. Anal. 49(6):4658-4703, 2017.
doi:10.1137/16M110229X |
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Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations,
Nonlinear Anal. 159:181-207, 2017.
doi:10.1016/j.na.2017.03.001 |
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Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space,
together with Claudia Raithel,
SIAM J. Math. Anal. 49(1):82-114, 2017.
doi:10.1137/16M1070384 |
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Sublinear growth of the corrector in stochastic homogenization: Optimal stochastic estimates for slowly decaying correlations,
together with Felix Otto,
Stochastics and Partial Differential Equations: Anal. Comp. 5(2):220-255, 2017.
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A higher-order large-scale regularity theory for random elliptic operators,
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Comm. Partial Differential Equations 41(7):1108-1148, 2016.
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Behaviour of free boundaries in thin-film flow: the regime of strong slippage and the regime of very weak slippage,
Ann. Inst. H. Poincaré Anal. Non Linéaire 33(5):1301-1327, 2016.
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Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form,
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SIAM J. Numer. Anal. 54(4):2359-2378, 2016.
doi:10.1137/15M1035379 |
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A posteriori modeling error estimates for the assumption of perfect incompressibility in the Navier-Stokes equation,
SIAM J. Numer. Anal. 53(5):2178-2205, 2015.
doi:10.1137/140966654 |
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Global existence of renormalized solutions to entropy-dissipating reaction-diffusion systems,
Arch. Ration. Mech. Anal. 218(1):553-587, 2015.
doi:10.1007/s00205-015-0866-x |
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Finite speed of propagation and waiting times for the stochastic porous medium equation - a unifying approach,
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SIAM J. Math. Anal. 47(1):825-854, 2015.
doi:10.1137/140960578 |
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Estimates on front propagation for nonlinear higher-order parabolic equations: an algorithmic approach,
Interfaces Free Bound. 17(1):1-20, 2015.
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Upper bounds on waiting times for the thin-film equation: the case of weak slippage,
Arch. Ration. Mech. Anal. 211(3):771-818, 2014.
doi:10.1007/s00205-013-0690-0
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Uniqueness of solutions of the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models,
Comm. Partial Differential Equations 38(11):2004-2047, 2013.
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Optimal lower bounds on asymptotic support propagation rates for the thin-film equation,
J. Differential Equations 255(10):3127-3149, 2013.
doi:10.1016/j.jde.2013.07.028
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Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models,
NoDEA Nonlinear Differential Equations Appl. 21(1):27-50, 2014.
doi:10.1007/s00030-013-0235-0
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Advection-driven support shrinking in a chemotaxis model with degenerate mobility,
SIAM J. Math. Anal. 45(3):1585-1615, 2013.
doi:10.1137/120874291 |