Julian Fischer
Personal Homepage
* = selected publication
  [36]     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., 2022.
*[35]     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.
*[34]     Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow,
together with Alice Marveggio,
submitted, 53 p., 2022.
  [33]     The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles,
together with Federico Cornalba,
submitted, 55 p., 2021.
  [32]     Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion,
together with Klemens Fellner, Michael Kniely, and Bao Quoc Tang,
submitted, 34 p., 2021.
*[31]     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,
submitted, 104 p., 2021.
  [30]     Quantitative normal approximation for sums of random variables with multilevel local dependence structure,
submitted, 2019.
  [29]     External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development,
together with Marcello Carioni and Anja Schlömerkemper,
in (minor) revision at J. Convex Anal., 2022.

Publications in Peer-Reviewed Journals
  [28]     Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation,
together with Nicola De Nitti,
Comm. Partial Differential Equations, 47(7):1394-1434, 2022.
  [27]     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.
  [26]     Scaling limit of the homogenization commutator for Gaussian coefficient fields,
together with Mitia Duerinckx and Antoine Gloria,
Ann. Appl. Probab., 32(2):1179-1209, 2022.
*[25]     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.
  [24]     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.
  [23]     The waiting time phenomenon in spatially discretized porous medium and thin film equations,
together with Daniel Matthes,
SIAM J. Numer. Anal. 59(1):60-87, 2021.
  [22]     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.
  [21]     Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,
together with Michael Kniely,
Nonlinearity 33:5733, 2020.
*[20]     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.
*[19]     The choice of representative volumes in the approximation of effective properties of random materials,
Arch. Ration. Mech. Anal. 234(2):635-726, 2019.
  [18]     Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with Lp data,
together with Olivier Kneuss,
J. Differential Equations 266:257-311, 2019.
  [17]     Existence of nonnegative solutions to stochastic thin-film equations,
together with Günther Grün,
SIAM J. Math. Anal. 50(1):411-455, 2018.
  [16]     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.
  [15]     Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations,
Nonlinear Anal. 159:181-207, 2017.
  [14]     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.
  [13]     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.
*[12]     A higher-order large-scale regularity theory for random elliptic operators,
together with Felix Otto,
Comm. Partial Differential Equations 41(7):1108-1148, 2016.
  [11]     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.
  [10]     Analysis of a modified second-order mixed hybrid BDM1 finite element method for transport problems in divergence form,
together with Fabian Brunner and Peter Knabner,
SIAM J. Numer. Anal. 54(4):2359-2378, 2016.
  [9]      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.
*[8]      Global existence of renormalized solutions to entropy-dissipating reaction-diffusion systems,
Arch. Ration. Mech. Anal. 218(1):553-587, 2015.
  [7]      Finite speed of propagation and waiting times for the stochastic porous medium equation - a unifying approach,
together with Günther Grün,
SIAM J. Math. Anal. 47(1):825-854, 2015.
  [6]      Estimates on front propagation for nonlinear higher-order parabolic equations: an algorithmic approach,
Interfaces Free Bound. 17(1):1-20, 2015.
*[5]      Upper bounds on waiting times for the thin-film equation: the case of weak slippage,
Arch. Ration. Mech. Anal. 211(3):771-818, 2014.
  [4]      Uniqueness of solutions of the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models,
Comm. Partial Differential Equations 38(11):2004-2047, 2013.
  [3]      Optimal lower bounds on asymptotic support propagation rates for the thin-film equation,
J. Differential Equations 255(10):3127-3149, 2013.
  [2]      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.
  [1]      Advection-driven support shrinking in a chemotaxis model with degenerate mobility,
SIAM J. Math. Anal. 45(3):1585-1615, 2013.

Reports, Proceedings, and Other
[P6]     Optimal-order estimates in stochastic homogenization: Beyond linear equations and smooth data,
Oberwolfach Report 11/2021.
[P5]     The choice of representative volumes for random materials,
Oberwolfach Report 56/2017.
[P4]     Appendix to the paper "Well-posedness for mean-field evolutions arising in superconductivity",
together with Mitia Duerinckx,
Ann. Inst. H. Poincaré Anal. Non Linéaire, 35(5):1267-1319, 2018.
[P3]     Approximation of slightly compressible fluids by the incompressible Navier-Stokes equation and linearized acoustics: a posteriori estimates,
Preprint, 2015.
[P2]     Global existence of renormalized solutions to entropy-dissipating reaction-diffusion systems,
Oberwolfach Report 51/2014.
[P1]     Optimal estimates on interface propagation in thin-film flow,
Oberwolfach Report 15/2013.

[T]      Optimal estimates on front propagation for the thin-film equation and other fourth-order parabolic equations,
PhD Thesis, 2013.
          Estimates on interface propagation rates for a degenerate chemotaxis model,
Master Thesis, 2011.