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math.AP2007
Wave equations on space-times of low regularity: Existence results and regularity theory in the framework of generalized function algebras
James D. E. Grant, Eberhard Mayerhofer
We present recent developments concerning Lorentzian geometry in algebras of generalized functions. These have, in particular, raised a new interest in refined regularity theory fo…
math-ph2007★ 12 cited
The wave equation on singular space-times
James D. E. Grant, Eberhard Mayerhofer, Roland Steinbauer
We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.
nlin.SI2007★ 11 cited
Multidimensional integrable systems and deformations of Lie algebra homomorphisms
Maciej Dunajski, James D. E. Grant, Ian A. B. Strachan
We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti--self--dual Yang--Mills equat…