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Lie symmetry of a class of nonlinear boundary value problems with free boundaries

Roman Cherniha, Sergii Kovalenko (2011)

Banach Center Publications

A class of (1 + 1)-dimensional nonlinear boundary value problems (BVPs), modeling the process of melting and evaporation of solid materials, is studied by means of the classical Lie symmetry method. A new definition of invariance in Lie's sense for BVP is presented and applied to the class of BVPs in question.

Limit formulas for groups with one conjugacy class of Cartan subgroups

Mladen Božičević (2008)

Annales de l’institut Fourier

Limit formulas for the computation of the canonical measure on a nilpotent coadjoint orbit in terms of the canonical measures on regular semisimple coadjoint orbits arise naturally in the study of invariant eigendistributions on a reductive Lie algebra. In the present paper we consider a particular type of the limit formula for canonical measures which was proposed by Rossmann. The main technical tool in our analysis are the results of Schmid and Vilonen on the equivariant sheaves on the flag variety...

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

Let H GL ( V ) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v V and let G = { g GL ( V ) g H v = H v } . Following Raïs we say that the orbit H v is characteristic for H if the identity component of G is H . If H is semisimple, we say that H v is semi-characteristic for H if the identity component of G is an extension of H by a torus. We classify the H -orbits which are not (semi)-characteristic in many cases.

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