Julian Fischer
Personal Homepage
Preprints
[22]     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, submitted, 2016.
[21]     Existence of nonnegative solutions to stochastic thin-film equations,
together with Günther Grün, submitted, 2016.
[20]     Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations,
submitted, 2016.
[19]     Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with Lp data,
together with Olivier Kneuss, submitted, 2016.
[18]     Approximation of slightly compressible fluids by the incompressible Navier-Stokes equation and linearized acoustics: a posteriori estimates,
Preprint, 2015.

Publications in Peer-Reviewed Journals
[17]     Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space,
together with Claudia Raithel, to appear in SIAM J. Math. Anal., 2016.
[16]     Sublinear growth of the corrector in stochastic homogenization: Optimal stochastic estimates for slowly decaying correlations,
together with Felix Otto, to appear in Stochastics and Partial Differential Equations: Anal. Comp., 2016.
[15]     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
[14]     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
[13]     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
[12]     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
[11]     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
[10]     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
[9]      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
[8]      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
[7]      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
[6]      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
[5]      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
[4]      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
[3]      Global existence of renormalized solutions to entropy-dissipating reaction-diffusion systems,
Oberwolfach Report 51/2014.
[2]      Optimal estimates on interface propagation in thin-film flow,
Oberwolfach Report 15/2013.

Theses
[1]      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.