Julian Fischer
Personal Homepage
* = selected publication
*[30]     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 Thilo Simon,
Preprint, 87 p., 2020.
  [29]     Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies,
together with Tim Laux and Thilo Simon,
submitted, 2020.
  [28]     A priori error analysis of a numerical stochastic homogenization method,
together with Dietmar Gallistl and Daniel Peterseim,
submitted, 2019.
  [27]     The waiting time phenomenon in spatially discretized porous medium and thin film equations, together with Daniel Matthes,
submitted, 2019.
  [26]     Scaling limit of the homogenization commutator for correlated coefficient fields,
together with Mitia Duerinckx and Antoine Gloria,
submitted, 2019.
  [25]     Quantitative normal approximation for sums of random variables with multilevel local dependence structure,
submitted, 2019.
  [24]     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,
submitted, 2019.
  [23]     Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model, together with Michael Kniely,
in (minor) revision at Nonlinearity, 2020.
*[22]     Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,
together with Stefan Neukamm,
in (minor) revision at Arch. Ration. Mech. Anal., 92 p., 2020.
  [21]     Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation,
together with Nicola De Nitti,
in (minor) revision at Comm. Partial Differential Equations, 2020.

Publications in Peer-Reviewed Journals
*[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
[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,
to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire, 2017.
[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.