arXiv subjects

Michael Kiessling

Publications and source records attributed to Michael Kiessling.

3 recordsLinked to original sources

arXiv2015

Constructing graphs over $R^n$ with small prescribed mean-curvature

In this paper a convergent series expansion is constructed to solve the prescribed mean curvature equation for n-dimensional hypersurfaces in n+1 dimensional Euclidean or Minkowskian space(time) which are graphs of a smooth real function u, and whose mean curvature function H is not too large in Hoelder norm, and integrable. Our approach is inspired by the Maxwell-Born-Infeld theory of electromagnetism in Minkowski spacetime, for which our method yields the first systematic way of explicitly computing the electrostatic potential u for regular charge densities proportional to H and small Born parameter.

math.AP↗

arXiv2005

The linear Fokker-Planck equation for the Ornstein-Uhlenbeck process as an (almost) nonlinear kinetic equation for an isolated N-particle system

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the infinite particle limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation.

math-ph↗

arXiv1998

Curl-Free Ginzburg-Landau Vortices

For certain nonlinear elliptic PDE problems in two dimensions, the classical isoperimetric inequality produces a sharp inequality that violates a Pohozaev identity except for radial symmetric, decreasing solutions. A generalized version of this technique is used here to prove radial symmetry of curl-free Ginzburg-Landau vortices.

math.AP↗