Bombach, ClemensClemensBombachGallaun, DennisDennisGallaunSeifert, ChristianChristianSeifertTautenhahn, MartinMartinTautenhahn2023-08-152023-08-152023-12-01Mathematical Control and Related Fields 13 (4): 1484-1499 (2023)https://hdl.handle.net/11420/42653We study (cost-uniform approximate) null-controllability of parabolic equations in Lp(Rd ) and provide explicit bounds on the control cost. In particular, we consider systems of the form ẋ(t) = −Apx(t) + 1E u(t), x(0) = x0 ∈ Lp(Rd ), with interior control on a so-called thick set E ⊂ Rd, where p ∈ [1, ∞), and where A is an elliptic operator of order m ∈ N in Lp(Rd ). We prove null-controllability of this system via duality and a sufficient condition for observability. This condition is given by an uncertainty principle and a dissipation estimate. Our result unifies and generalizes earlier results obtained in the context of Hilbert and Banach spaces. In particular, our result applies to the case p = 1.en2156-84992023414841499Banach spaceC -semigroups 0elliptic operatorsL -spaces pnon-reflexiveNull-controllabilityobservability estimateMathematicsJournal Article10.3934/mcrf.2022046Journal Article