BCAM Seminar The Hardy inequality and the asymptotic behaviour of the heat equation in twisted domains
Data: Az, Urt 21 2009
Lekua: Academy of Mathematics and Systems Sciences,Chinese Academy of Sciences China
Hizlariak: Xu ZHANG
In this talk we revise a recently established Hardy inequality in twisted tubes on the background of transience of the Brownian motion.
We begin by recalling the classical Hardy inequality and its relation to geometric, spectral, stochastic and other properties of the underlying Euclidean space. After discussing the complexity of the problem when reformulated for quasi-cylindrical subdomains, we focus on the prominent class of tubes. As the main result, we show that the geometric deformation of twisting yields an improved decay rate for solutions of the heat equation in three-dimensional tubes ofuniform cross-section. This is a joint work with Enrique Zuazua.
We begin by recalling the classical Hardy inequality and its relation to geometric, spectral, stochastic and other properties of the underlying Euclidean space. After discussing the complexity of the problem when reformulated for quasi-cylindrical subdomains, we focus on the prominent class of tubes. As the main result, we show that the geometric deformation of twisting yields an improved decay rate for solutions of the heat equation in three-dimensional tubes ofuniform cross-section. This is a joint work with Enrique Zuazua.