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日時: 2012年10月12日(金) 16:30〜17:30
会場: 東京大学 大学院数理科学研究科 123号室
Antonio Siconolfi 氏 (La Sapienza - University of Rome)
Homogenization on arbitrary manifolds
We show that results on periodic homogenization for Hamilton-Jacobi equations can be generalized replacing the torus by an arbitrary compact manifold. This allows to reach a deeper understanding of the matter and unveils phenomena somehow hidden in the periodic case, for instance the fact that the ambient spaces of oscillating equations and that of the limit problem are different, and possess even different dimensions. Repetition structure for the base manifold, changes of scale in it and asymptotic analysis, which are the basic ingredients of homogenization, need substantial modification to work in the new frame, and this task is partially accomplished using tools from algebraic topology. An adapted notion of convergence allowing approximating entities and limit to lie in different spaces is also provided.