Optimal elliptic Sobolev regularity near three-dimensional, multi-material Neumann vertices

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

Keywords

Elliptic div-grad operators, anisotropic ellipticity in three dimensions, transmission at material interfaces, mixed Dirichlet-Neumann boundary conditions, optimal Sobolev regularity

URI

https://doi.org/10.34657/2953
https://oa.tib.eu/renate/handle/123456789/2305

Citation

Haller-Dintelmann, R., Höppner, W., Kaiser, H.-C., Rehberg, J., & Ziegler, G. M. (2010). Optimal elliptic Sobolev regularity near three-dimensional, multi-material Neumann vertices (Vol. 1515). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

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Mathematik

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