On the Dirichlet and Neumann evolution operators in R^d₊

2013/07/20 by Luciana Angiuli, Angiuli, Luciana, Luca Lorenzi +1
Mathematics · #35B40 #35K10 #35K15 #37L40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35K10 #msc:35K15 #msc:37L40

paper · pdf · doi:10.48550/arxiv.1307.5447

arxiv created 2013/07/20 · arxiv updated 2013/07/23

Abstract

We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators G_D(t,s) and G_N(t,s) associated with a class of nonautonomous elliptic operators \A(t) with unbounded coefficients defined in I× \Rd₊ (where I is a right-halfline or I=\R). We also prove the existence and the uniqueness of a tight evolution system of measures \μ_t^N\_{t ∈ I} associated with G_N(t,s), which turns out to be sub-invariant for G_D(t,s), and we study the asymptotic behaviour of the evolution operators G_D(t,s) and G_N(t,s) in the L^p-spaces related to the system \μ_t^N\_{t ∈ I}.

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