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Hardy inequalities, observability, and control for the wave and Schrödinger equations with singular potentials. (English) Zbl 1200.35008

Wave equation and Schrödinger equation perturbed by a singular-square potential are considered. Using the method of multipliers, the authors prove exact boundary controllability in the range of subcritical coefficients of the singular potential and under suitable geometric conditions. The supercritical case is also analyzed.

MSC:

35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
93B07 Observability
35Q41 Time-dependent Schrödinger equations and Dirac equations
35L05 Wave equation
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