F Ur Mathematik in Den Naturwissenschaften Leipzig Regularity and Optimal Design Results for Elastic Membranes Regularity and Optimal Design Results for Elastic Membranes

F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig

We provide a new proof of a regularity theorem for systems of nonlinear elliptic equations with the quadratic nonlinearity in dimension two.

für Mathematik in den Naturwissenschaften Leipzig

Motivated by relaxation in the calculus of variations, this paper addresses convex but not necessarily strictly convex minimization problems. A class of energy functionals is described for which any stress field σ in L(Ω) with div σ in W 1,p ′ (Ω) (from Euler Lagrange equations and smooth lower order terms) belongs to W 1,q loc (Ω). Applications include the scalar double-well potential, an opti...

Max - Planck - Institut für Mathematik in den Naturwissenschaften Leipzig Representation of Markov chains by random

We systematically investigate the problem of representing Markov chains by families of random maps, and what regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translat...

Mathematik in den Naturwissenschaften Leipzig C 1 , α Regularity for Solutions to the p - Harmonic thin Obstacle Problem

We prove C regularity for a thin obstacle problem for the p-laplace equation. Due to the nonlinearity of the p-laplace operator we can not use the same methods used for the Laplace case, instead we use techniques developed by E. de Giorgi. AMS Classification: 35R35, 35J60, 35B65.

F Ur Mathematik in Den Naturwissenschaften Leipzig Interacting Quantum Fields on a Curved Background