 2015Herbert Koch and Stefan Steinerberger
Convolution Estimates for Singular Measures and Some Global Nonlinear BrascampLieb Inequalities
Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 145(6): 12231237 2015
http://arxiv.org/abs/1404.4536
Abstract: We give an L2 x L2 → L2 convolution estimate for singular measures supported on transversal hypersurfaces in ℝn, which improves earlier results of Bejenaru et al. as well as Bejenaru and Herr. The quantities arising are relevant to the study of the validity of bilinear estimates for dispersive partial differential equations. We also prove a class of global, nonlinear Brascamp–Lieb inequalities with explicit constants in the same spirit. 
 
 Herbert Koch, Angkana Rüland and Wenhui Shi
The Variable Coefficient Thin Obstacle Problem: Optimal Regularity and Regularity of the Regular Free Boundary
2015
http://arXiv.org/abs/1504.03525

 
 Herbert Koch
Selfsimilar solutions to supercritical gKdV
Nonlinearity, 28(3): 545575 2015
http://dx.doi.org/10.1088/09517715/28/3/545

 
 Jan Maas and Daniel Matthes
Longtime behavior of a finite volume discretization for a fourth order diffusion equation
ArXiv eprints 2015
http://arxiv.org/abs/1505.03178

 
 Barbara Niethammer, Sebastian Throm and Juan J. L. Velázquez
A revised proof of uniqueness of selfsimilar profiles to Smoluchowski's coagulation equation for kernels close to constant
2015
http://arxiv.org/abs/1510.03361

 
 Barbara Niethammer, Juan J. L. Velázquez and Michael Helmers
Mathematical analysis of a coarsening model with local interactions
2015
http://arxiv.org/abs/1509.04917

 
 Barbara Niethammer, Sebastian Throm and Juan J. L. Velázquez
Selfsimilar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels
Ann. I. H. Poincaré  AN 2015
http://dx.doi.org/10.1016/j.anihpc.2015.04.002

 
 Celia Reina, Anja Schlömerkemper and Sergio Conti
Derivation of F=FeFp as the continuum limit of crystalline slip
preprint 2015
http://arxiv.org/abs/1504.06775
Abstract: In this paper we provide a proof of the multiplicative kinematic description of crystal elastoplasticity in the setting of large deformations, i.e.~$\F=\Fe\Fp$ for a two dimensional single crystal. The proof starts by considering a general configuration at the mesoscopic scale, where the dislocations are discrete line defects (points in the twodimensional description used here) and the displacement field can be considered continuous everywhere in the domain except at the slip surfaces, over which there is a displacement jump. At such scale, as previously shown by two of the authors, there exists unique physicallybased definitions of the total deformation tensor $\F$ and the elastic and plastic tensors $\Fe$ and $\Fp$ that do not require the consideration of any nonrealizable intermediate configuration and do not assume any a priori relation between them of the form $\F=\Fe\Fp$. This mesoscopic description is then passed to the continuum limit via homogenization i.e., by increasing the number of slip surfaces to infinity and reducing the lattice parameter to zero. We show for twodimensional deformations of initially perfect single crystals that the classical continuum formulation is recovered in the limit with $\F=\Fe\Fp$, $\det \Fp= 1$ and $\mathbfG=\textCurl\ \Fp$ the dislocation density tensor. 
 
 Angkana Rüland
Unique continuation for fractional Schrödinger equations with rough potentials
Comm. Partial Differential Equations, 40(1): 77114 2015
http://dx.doi.org/10.1080/03605302.2014.905594

 
 Martin Rumpf and Benedikt Wirth
Variational time discretization of geodesic calculus
IMA J. Numer. Anal., 35(3): 10111046 2015
http://dx.doi.org/10.1093/imanum/dru027
Abstract: We analyze a variational time discretization of geodesic calculus on finite and certain classes of infinitedimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete logarithm, discrete exponential maps, and discrete parallel transport, and we prove convergence to their continuous counterparts. The presented analysis is based on the direct methods in the calculus of variation, on convergence, and on weighted finite element error estimation. The convergence results of the discrete geodesic calculus are experimentally confirmed for a basic model on a twodimensional Riemannian manifold. This provides a theoretical basis for the application to shape spaces in computer vision, for which we present one specific example. 
 
 Brandon Runnels, Irene Beyerlein, Sergio Conti and Michael Ortiz
A relaxation method for the energy and morphology of grain boundaries and interfaces
J. Mech. Phys. Solids 2015
http://dx.doi.org/10.1016/j.jmps.2015.11.007

 
 Stefan Steinerberger
Dispersion dynamics for the defocusing generalized Kortewegde Vries equation
Proc. Amer. Math. Soc., 143(2): 789800 2015
http://dx.doi.org/10.1090/S000299392014122854

 
 KarlTheodor Sturm
Metric Measure Spaces with Variable Ricci Bounds and Couplings of Brownian Motions
In ZhenQing Chen, Niels Jacob, Masayoshi Takeda, Toshihiro Uemura, editor, Festschrift Masatoshi Fukushima, Volume 17 of Interdisciplinary Mathematical Sciences
Chapter 27, page 553575.
2015
http://dx.doi.org/10.1142/9789814596534_0027
Abstract: The goal of this paper is twofold: we study metric measure spaces (X, d, m) with variable lower bounds for the Ricci curvature and we study pathwise coupling of Brownian motions. Given any lower semicontinuous function k : X → ℝ we introduce the curvaturedimension condition CD(k, ∞) which canonically extends the curvaturedimension condition CD(K, ∞) of LottSturmVillani for constant K ∈ R. For infinitesimally Hilbertian spaces we prove
its equivalence to an evolutionvariation inequality EVIk which in turn extends the EVIKinequality of AmbrosioGigliSavaré;
its stability under convergence and its localtoglobal property.
For metric measure spaces with uniform lower curvature bounds K we prove that for each pair of initial distributions µ1, µ2 on X there exists a coupling , t ≥ 0, of two Brownian motions on X with the given initial distributions such that a.s. 
 
 Juan J. L. Velázquez and Arthur H. M. Kierkels
On selfsimilar solutions to a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation
2015
http://arxiv.org/abs/1511.01292

 
 Juan J. L. Velázquez and Miguel Escobedo
On the theory of Weak Turbulence for the Nonlinear Schrödinger Equation
Memoirs of the AMS, 238 2015
http://dx.doi.org/10.1090/memo/1124
Abstract: We study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. We define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. We also prove the existence of a family of solutions that exhibit pulsating behavior. 
 
 Juan J. L. Velázquez and Jogia Bandyopadhyay
Blowup rate estimates for the solutions of the bosonic BoltzmannNordheim equation
J. Math. Phys., 56(Art. 063302): 129 2015
http://arxiv.org/abs/1411.5460
Abstract: In this paper, we study the behavior of a class of mild solutions of the homogeneous and isotropic bosonic BoltzmannNordheim equation near the blowup. We obtain some estimates on the blowup rate of the solutions and prove that, as long as a solution is bounded above by the critical singularity 1x1x (the equilibrium solutions behave like this power law near the origin), it remains bounded in the uniform norm. In Sec. III of the paper, we prove a local existence result for a class of measurevalued mild solutions, which is of independent interest and which allows us to solve the BoltzmannNordheim equation for some classes of unbounded densities. 
 
 Christian Zillinger
Linear inviscid damping for monotone shear flows in a finite periodic channel, boundary effects, blowup and critical Sobolev regularity
Archive for Rational Mechanics and Analysis 2015
http://link.springer.com/article/10.1007/s0020501609911

 
 2014Sebastian Andres, JeanDominique Deuschel and Martin Slowik
Heat kernel estimates for random walks with degenerate weights
2014
http://arxiv.org/abs/1412.4338

 
 Gerard Barkema, Patrik L. Ferrari, Joel L. Lebowitz and Herbert Spohn
KPZ universality class and the anchored Toom interface
Phys. Rev. E, 90(Art. 042116) 2014
http://dx.doi.org/10.1103/PhysRevE.90.042116
Abstract: We revisit the anchored Toom interface and use KPZ scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. There is no free parameter. The predictions are numerically well confirmed for spacetime statistics in the stationary state. In particular the spatial fluctuations of the interface are given by the GOE edge distribution of Tracy and Widom. 
 
 Mario Bebendorf
Lowrank approximation of elliptic boundary value problems with highcontrast coefficients
2014
http://arxiv.org/abs/1410.3717

 