Vancostenoble J, Zuazua E (2009)
Publication Type: Journal article
Publication year: 2009
Book Volume: 41
Pages Range: 1508-1532
Journal Issue: 4
DOI: 10.1137/080731396
We address the question of exact controllability of the wave and Schrodinger equations perturbed by a singular inverse-square potential. Exact boundary controllability is proved in the range of subcritical coefficients of the singular potential and under suitable geometric conditions. The proof relies on the method of multipliers. The key point in the proof of the observability inequality is a suitable Hardy-type inequality with sharp constants. On the contrary, in the supercritical case, we prove that exact controllability is false.
APA:
Vancostenoble, J., & Zuazua, E. (2009). HARDY INEQUALITIES, OBSERVABILITY, AND CONTROL FOR THE WAVE AND SCHRODINGER EQUATIONS WITH SINGULAR POTENTIALS. SIAM Journal on Mathematical Analysis, 41(4), 1508-1532. https://doi.org/10.1137/080731396
MLA:
Vancostenoble, J., and Enrique Zuazua. "HARDY INEQUALITIES, OBSERVABILITY, AND CONTROL FOR THE WAVE AND SCHRODINGER EQUATIONS WITH SINGULAR POTENTIALS." SIAM Journal on Mathematical Analysis 41.4 (2009): 1508-1532.
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