On checking L^p-admissibility for parabolic control systems
arxiv(2024)
摘要
In this note we discuss the difficulty of verifying
L^p-admissibility for p≠ 2 – that even manifests in the
presence of a self-adjoint semigroup generator on a Hilbert space – and survey
tests for L^p-admissibility of given control operators. These tests
are obtained by virtue of either mapping properties of boundary trace
operators, yielding a characterization of admissibility via abstract
interpolation spaces; or through Laplace–Carleson embeddings, slightly
extending results from Jacob, Partington and Pott to a class of systems which
are not necessarily diagonal with respect to sequence spaces. Special focus is
laid on illustrating the theory by means of examples based on the heat equation
on various domains.
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