66 citations · 149 across the 23 of their papers we have counts for
28 papers
Regularity theorems for random elliptic operators on domains
Peter Bella, Julian Fischer, Marc Josien +1
Regularity theorems à la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random ellip…
Density fluctuations in weakly interacting particle systems via the Dean-Kawasaki equation
Federico Cornalba, Julian Fischer, Jonas Ingmanns +1
The Dean-Kawasaki equation - one of the most fundamental SPDEs of fluctuating hydrodynamics - has been proposed as a model for density fluctuations in weakly interacting particle s…
Local minimizers of the interface length functional based on a concept of local paired calibrations
Julian Fischer, Sebastian Hensel, Tim Laux +1
We establish that regular flat partitions are locally minimizing for the interface energy with respect to perturbations of the phases. Regular flat partitions are partitions…
Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow
Julian Fischer, Alice Marveggio
Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scalin…
A monotonicity formula for minimizers of the Mumford-Shah functional in 2d and a sharp lower bound on the energy density
Julian Fischer
We establish a new monotonicity formula for minimizers of the Mumford-Shah functional in planar domains. Our formula follows the spirit of Bucur-Luckhaus, but works with the David-…
Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion
Klemens Fellner, Julian Fischer, Michael Kniely +1
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to ha…
The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles
Federico Cornalba, Julian Fischer
The Dean-Kawasaki equation - a strongly singular SPDE - is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuation…
Global existence analysis of energy-reaction-diffusion systems
Julian Fischer, Katharina Hopf, Michael Kniely +1
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest…
The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions
Julian Fischer, Sebastian Hensel, Tim Laux +1
We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniquen…
Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies
Julian Fischer, Tim Laux, Theresa M. Simon
We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter…
A priori error analysis of a numerical stochastic homogenization method
Julian Fischer, Dietmar Gallistl, Daniel Peterseim
This paper provides an a~priori error analysis of a localized orthogonal decomposition method (LOD) for the numerical stochastic homogenization of a model random diffusion problem.…
The waiting time phenomenon in spatially discretized porous medium and thin film equations
Julian Fischer, Daniel Matthes
Various degenerate diffusion equations exhibit a waiting time phenomenon: Dependening on the "flatness" of the compactly supported initial datum at the boundary of the support, the…
Scaling limit of the homogenization commutator for Gaussian coefficient fields
Mitia Duerinckx, Julian Fischer, Antoine Gloria
Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution operator displays fluctuations around its expectation. The…
Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems
Julian Fischer, Stefan Neukamm
We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone ope…
Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation
Nicola De Nitti, Julian Fischer
We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distrib…
Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model
Julian Fischer, Michael Kniely
In the computation of the material properties of random alloys, the method of "special quasirandom structures" attempts to approximate the properties of the alloy on a finite volum…
Quantitative normal approximation for sums of random variables with multilevel local dependence structure
Julian Fischer
We establish a quantitative normal approximation result for sums of random variables with multilevel local dependencies. As a corollary, we obtain a quantitative normal approximati…
Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension
Julian Fischer, Sebastian Hensel
In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension - like, for example, the evolution of oil bubbles in…
External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a -development
Marcello Carioni, Julian Fischer, Anja Schlömerkemper
This paper is concerned with equilibrium configurations of one-dimensional particle system with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its pass…
The choice of representative volumes in the approximation of effective properties of random materials
Julian Fischer
The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: A sample of the ran…
Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations
Julian Fischer
We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation e…
Stochastic homogenization of linear elliptic equations: Higher-order error estimates in weak norms via second-order correctors
Peter Bella, Benjamin Fehrman, Julian Fischer +1
We are concerned with the homogenization of second-order linear elliptic equations with random coefficient fields. For symmetric coefficient fields with only short-range correlatio…
Well-posedness for mean-field evolutions arising in superconductivity
Mitia Duerinckx
We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in a joint work with Serfaty in certain regimes as the mean-field evolu…
Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space
Julian Fischer, Claudia Raithel
We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for…