2010, Haller-Dintelmann, Robert, Höppner, Wolfgang, Kaiser, Hans-Christoph, Rehberg, Joachim, Ziegler, Günter M.

We study relative stability properties of different clusters of closely packed one- and two-dimensional localized peaks of the Swift-Hohenberg equation. We demonstrate the existence of a 'spatial Maxwell' point where clusters are almost equally stable, irrespective of the number of pes involved. Above (below) the Maxwell point, clusters become more (less) stable with the increase of the number of peaks

2010, Kaiser, Hans-Christoph, Rehberg, Joachim

We investigate optimal elliptic regularity of anisotropic div-grad operators in three dimensions at the crossing of a material interface and an edge of the spatial domain on the Neumann boundary part within the scale of Sobolev spaces.