We consider the parabolic Lamé system on a bounded domain. We focus on two types of inequalities for higher-order derivatives of solutions. The first is related to an Lᵖ L p - Lᵖ L p estimate locally in time in the Lebesgue space setting, which includes the endpoint cases $$p=1$$ p = 1 and p=∞ p = ∞ . The second concerns an equivalent norm of Besov spaces by means of the solution of the parabolic Lamé system.
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Furuto et al. (2026) studied this question.
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