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 × R^d_+ (where I is a right-halfline or I = R). We also prove the existence and the uniqueness of a tight evolution system of measures {mu_t^N}_{t\in I} associated with G^N(t, s), which turns out to be subinvariant 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 {mu_t^N}_{t\in I}.
On the Dirichlet and Neumann Evolution Operators in R^d_+ / L., Angiuli; Lorenzi, Luca Francesco Giuseppe. - In: POTENTIAL ANALYSIS. - ISSN 1572-929X. - 41:4(2014), pp. 1079-1110. [10.1007/s11118-014-9406-9]
On the Dirichlet and Neumann Evolution Operators in R^d_+
LORENZI, Luca Francesco Giuseppe
2014-01-01
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 × R^d_+ (where I is a right-halfline or I = R). We also prove the existence and the uniqueness of a tight evolution system of measures {mu_t^N}_{t\in I} associated with G^N(t, s), which turns out to be subinvariant 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 {mu_t^N}_{t\in I}.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
