Preprints - IAM Publications


	2017 Herbert Koch and Junfeng Li Global well-posedness and scattering for small data for the three-dimensional Kadomtsev--Petviashvili II equation Communications in Partial Differential Equations, 42(6): 950--976 2017 https://doi.org/10.1080/03605302.2017.1320410

	2016 Stefan Adams, Roman Kotecký and Stefan Müller Strict Convexity of the Surface Tension for Non-convex Potentials 2016 http://arxiv.org/abs/1606.09541v1

	Patrick Gérard and Herbert Koch The cubic Szegő flow at low regularity Séminaire Laurent SchwartzâÉquations aux dérivées partielles et applications. Année, 2017 2016 http://slsedp.cedram.org/item?id=SLSEDP_2016-2017____A14_0

	A.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: 820--866 2016 http://dx.doi.org/10.1016/j.aim.2016.06.023

	2015 Sebastian 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/s00440-015-0670-4

	Louis-Pierre 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): 557--569 2015 http://dx.doi.org/10.1214/14-AIHP608

	Tristan Buckmaster and Herbert Koch The Korteweg--de Vries equation at H- 1 regularity Ann. I. H. Poincaré - AN, 32: 1071-1098 2015 http://dx.doi.org/10.1016/j.anihpc.2014.05.004 Abstract: In this paper we will prove the existence of weak solutions to the Korteweg-de Vries initial value problem on the real line with H^-1 initial data; moreover, we will study the problem of orbital and asymptotic H^s stability of solitons for integers s≥ -1; finally, we will also prove new a priori H^-1 bounds for solutions to the Korteweg-de Vries equation. The paper will utilise the Miura transformation to link the Korteweg-de Vries equation to the modified Korteweg-de Vries equation.

	Matthias Erbar, Kazumasa Kuwada and Karl-Theodor Sturm On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces Invent. Math., 201(3): 993-1071 2015 http://dx.doi.org/10.1007/s00222-014-0563-7

	Lisa B. Hartung and Anton Klimovsky The glassy phase of the complex branching Brownian motion energy model Electron. Commun. Probab., 20(Art. 78): 1-15 2015 http://dx.doi.org/10.1214/ECP.v20-4360

	Christian Ketterer Evolution variational inequality and Wasserstein control in variable curvature context ArXiv e-prints 2015 http://arxiv.org/abs/1509.02178

	Christian Ketterer On the geometry of metric measure spaces with variable curvature bounds ArXiv e-prints 2015 http://arxiv.org/abs/1506.03279

	Christian Ketterer Cones over metric measure spaces and the maximal diameter theorem J. Math. Pures Appl. (9), 103(5): 1228-1275 2015 http://dx.doi.org/10.1016/j.matpur.2014.10.011

	Christian Ketterer Obata's Rigidity Theorem for Metric Measure Spaces Anal. Geom. Metr. Spaces, 3(Art. 16): 278-295 2015 http://dx.doi.org/10.1515/agms-2015-0016

	Arthur H. M. Kierkels and Juan J. L. Velázquez On the transfer of energy towards infinity in the theory of weak turbulence for the nonlinear Schrödinger equation J. Stat. Phys., 159(3): 668-712 2015 http://dx.doi.org/10.1007/s10955-015-1194-0 Abstract: We study the mathematical properties of a kinetic equation which describes the long time behaviour of solutions to the weak turbulence equation associated to the cubic nonlinear Schrödinger equation.In particular, we give a precise definition of weak solutions and prove global existence of solutions for all initial data with finite mass. We also prove that any nontrivial initial datum yields the instantaneous onset of a condensate, i.e.~a Dirac mass at the origin for any positive time. Furthermore we show that the only stationary solutions with finite total measure are Dirac masses at the origin. We finally construct solutions with finite energy, which is transferred to infinity in a self-similar manner.

	Herbert Koch and Nikolai Nadirashvili Partial analyticity and nodal sets for nonlinear elliptic systems 2015 http://arxiv.org/abs/1506.06224

	Herbert Koch and Stefan Steinerberger Convolution Estimates for Singular Measures and Some Global Nonlinear Brascamp-Lieb Inequalities Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 145(6): 1223-1237 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 Self-similar solutions to super-critical gKdV Nonlinearity, 28(3): 545-575 2015 http://dx.doi.org/10.1088/0951-7715/28/3/545

	Juan J. L. Velázquez and Arthur H. M. Kierkels On self-similar solutions to a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation 2015 http://arxiv.org/abs/1511.01292

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