Julian Fischer
Personal Homepage
Preprints
[23]     Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension, together with Sebastian Hensel,
submitted, 2018.
[22]     The choice of representative volumes for random materials,
submitted, 2018.
[21]     Quantitative normal approximation for sums of random variables with multilevel local dependence structure,
Preprint, 2019.
[20]     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, 2018.
[19]     Approximation of slightly compressible fluids by the incompressible Navier-Stokes equation and linearized acoustics: a posteriori estimates,
Preprint, 2015.

Publications in Peer-Reviewed Journals
[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.
doi:10.1016/j.jde.2018.07.045
[17]     Existence of nonnegative solutions to stochastic thin-film equations,
together with Günther Grün,
SIAM J. Math. Anal. 50(1):411-455, 2018.
doi:10.1137/16M1098796
[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.
doi:10.1137/16M110229X
[15]     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
[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.
doi:10.1137/16M1070384
[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.
doi:10.1007/s40072-016-0086-x
[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.
doi:10.1080/03605302.2016.1179318
[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.
doi:10.1016/j.anihpc.2015.05.001
[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.
doi:10.1137/15M1035379
[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.
doi:10.1137/140966654
[8]      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
[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.
doi:10.1137/140960578
[6]      Estimates on front propagation for nonlinear higher-order parabolic equations: an algorithmic approach,
Interfaces Free Bound., 17(1):1-20, 2015.
doi:10.4171/IFB/331
[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.
doi:10.1007/s00205-013-0690-0
[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.
doi:10.1080/03605302.2013.823548
[3]      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
[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.
doi:10.1007/s00030-013-0235-0
[1]      Advection-driven support shrinking in a chemotaxis model with degenerate mobility,
SIAM J. Math. Anal., 45(3):1585-1615, 2013.
doi:10.1137/120874291

Reports and Proceedings
[P4]     The choice of representative volumes for random materials,
Oberwolfach Report 56/2017.
[P3]     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.
doi:j.anihpc.2017.11.004
[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.

Theses
[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.