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Carleman inequalities for the two-dimensional heat equation in singular domains

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  • We consider the Cauchy problem associated to the heat equation firstly in a plane domain with a reentrant corner, then in a cracked domain. By constructing a weight function, we prove a Carleman inequality and we deduce a result of controllability.
    Mathematics Subject Classification: Primary: 95B05, 35J30, 35B65, 35B25, 35J25.

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