Let A be the generator of an analytic semigroup T on L2(Ω), where Ω is a homogeneous space with doubling property. We prove maximal Lp - Lq a-priori estimates for the solution of the parabolic evolution equation u′(t) = Au(t) + f(t), u(0) = 0 provided T may be represented by a heat-kernel satisfying certain bounds (and in particular a Gaussian bound).
|ジャーナル||Communications in Partial Differential Equations|
|出版ステータス||Published - 1997|
ASJC Scopus subject areas
- Applied Mathematics