 2016A.H.M. Kierkels
On a kinetic equation in weak turbulence theory for the nonlinear Schrödinger equation
2016
http://arxiv.org/abs/1606.07290

 
 Herbert Koch, Angkana Rüland and Wenhui Shi
The variable coefficient thin obstacle problem: Carleman inequalities
Adv. Math., 301: 820866 2016
http://dx.doi.org/10.1016/j.aim.2016.06.023

 
 P. Laurençot, B. Niethammer and J. J. L. Velázquez
Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel
2016
http://arxiv.org/abs/1603.02929

 
 Jan Maas, Martin Rumpf and Stefan Simon
Generalized optimal transport with singular sources
2016
http://arxiv.org/abs/1607.01186

 
 Patrick Müller
Path large deviations for interacting diffusions with local meanfield interactions
2016
http://arxiv.org/abs/1512.05323
Abstract: We consider a system of Nd spins, with a local mean field type interaction. Each spin has a fixed spacial position on the torus Td and a spin value in R that evolves according to a space dependent Langevin dynamic. The interaction between two spins depends on their spacial distance. We investigate the path large deviation principle from the hydrodynamic (or local mean field McKeanVlasov) limit and characterise the rate function, for both the space dependent empirical process and the space dependent empirical measure of the paths. To this end, we generalize an approach of Dawson and G\"artner. By the space dependency, this requires new ingredients compared to mean field type interactions. Moreover, we prove the large deviation principle by using second approach. This requires a generalisation of Varadhan's lemma to nowhere continuous functions. 
 
 A. Nota and J.J.L. Velázquez
On the growth of a particle coalescing in a Poisson distribution of obstacles
2016
http://arxiv.org/abs/1608.08118

 
 Alan D. Rendall and Juan J. L. Velázquez
Veiled singularities for the spherically symmetric massless EinsteinVlasov system
2016
http://arxiv.org/abs/1604.06576

 
 Angkana Rüland, Christian Zillinger and Barbara Zwicknagl
Higher Sobolev regularity of convex integration solutions in elasticity
2016
https://arxiv.org/abs/1610.02529

 
 2015Sebastian Andres and Naotaka Kajino
Continuity and estimates for the Liouville heat kernel with applications to spectral dimensions
Probab. Theory Relat. Fields 2015
http://dx.doi.org/10.1007/s0044001506704

 
 Sebastian Andres, JeanDominique Deuschel and Martin Slowik
Harnack inequalities on weighted graphs and some applications to the random conductance model
Probab. Theory Relat. Fields: 147 2015
http://dx.doi.org/10.1007/s004400150623y
Abstract: We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk X in an environment of ergodic random conductances taking values in (0,∞) satisfying some moment conditions. 
 
 Sebastian Andres, JeanDominique Deuschel and Martin Slowik
Invariance principle for the random conductance model in a degenerate ergodic environment
Ann. Probab., 43(4): 18661891 2015
http://dx.doi.org/10.1214/14AOP921

 
 LouisPierre Arguin, Anton Bovier and Nicola Kistler
An ergodic theorem for the extremal process of branching Brownian motion
Ann. Inst. Henri Poincaré Probab. Stat., 51(2): 557569 2015
http://dx.doi.org/10.1214/14AIHP608

 
 Mathias Beiglböck, Martin Huesmann and Florian Stebegg
Root to Kellerer
ArXiv eprint 2015
http://arxiv.org/abs/1507.07690

 
 Mathias Beiglböck, Alexander M. G. Cox, Martin Huesmann, Nicolas Perkowski and David J. Prömel
Pathwise superreplication via Vovk's outer measure
ArXiv eprints 2015
http://arxiv.org/abs/1504.03644

 
 Peter Bella, Michael Goldman and Barbara Zwicknagl
Study of Island Formation in Epitaxially Strained Films on Unbounded Domains
Arch. for Ration. Mech. and Anal., 218(1): 163217 2015
http://dx.doi.org/10.1007/s002050150858x

 
 Benjamin Berkels, Alexander Effland and Martin Rumpf
A Posteriori Error Control for the Binary MumfordShah Model
ArXiv Preprint 2015
http://arxiv.org/abs/1505.05284
Abstract: The binary MumfordShah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented region. To this end, a suitable strictly convex and nonconstrained relaxation of the originally nonconvex functional is investigated and Repin's functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the $L^2$norm. In combination with a suitable cut out argument, a fully practical estimate for the area mismatch is derived. This estimate is incorporated in an adaptive meshing strategy. Two different adaptive primaldual finite element schemes, and the most frequently used finite difference discretization are investigated and compared. Numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications. 
 
 Benjamin Berkels, Alexander Effland and Martin Rumpf
Time Discrete Geodesic Paths in the Space of Images
SIAM J. Imaging Sci., 8(3): 14571488 2015
http://dx.doi.org/10.1137/140970719
Abstract: In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and effective variational time discretization of geodesics paths is proposed. This requires to minimize a discrete path energy consisting of a sum of consecutive image matching functionals over a set of image intensity maps and pairwise matching deformations. For squareintegrable input images the existence of discrete, connecting geodesic paths defined as minimizers of this variational problem is shown. Furthermore, Γconvergence of the underlying discrete path energy to the continuous path energy is proved. This includes a diffeomorphism property for the induced transport and the existence of a squareintegrable weak material derivative in space and time. A spatial discretization via finite elements combined with an alternating descent scheme in the set of image intensity maps and the set of matching deformations is presented to approximate discrete geodesic paths numerically. Computational results underline the efficiency of the proposed approach and demonstrate important qualitative properties.

 
 S. Beuchler, K. Hofer, D. Wachsmuth and J.E. Wurst
Boundary concentrated finite elements for optimal control problems with distributed observation
Comput. Optim. Appl., 62(1): 3165 2015
http://dx.doi.org/10.1007/s1058901597375

 
 Alexei Borodin and Patrik L. Ferrari
Random tilings and Markov chains for interlacing particles
ArXiv eprints 2015
http://arxiv.org/abs/1506.03910

 
 David Bourne, Sergio Conti and Stefan Müller
Energy bounds for a compressed elastic film on a substrate
preprint 2015
http://arxiv.org/abs/1512.07416
Abstract: We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, describing the two main physical effects. The first part represents the elastic energy of the film, which is approximated using the von Kármán plate theory. The second part represents the fracture or delamination energy, which is approximated using the Griffith model of fracture. A simpler model containing the first term alone was previously studied with similar methods by several authors, assuming that the delaminated region is fixed. We include the fracture term, transforming the elastic minimization into a freeboundary problem, and opening the way for patterns which result from the interplay of elasticity and delamination. After rescaling, the energy depends on only two parameters: the rescaled film thickness, $σ$, and a measure of the bonding strength between the film and substrate, $γ$. We prove upper bounds on the minimum energy of the form $σ^a γ^b$ and find that there are four different parameter regimes corresponding to different values of $a$ and $b$ and to different folding patterns of the film. In some cases the upper bounds are attained by selfsimilar folding patterns as observed in experiments. Moreover, for two of the four parameter regimes we prove matching, optimal lower bounds. 
 