HARDY INEQUALITIES, OBSERVABILITY, AND CONTROL FOR THE WAVE AND SCHRODINGER EQUATIONS WITH SINGULAR POTENTIALS

Vancostenoble J, Zuazua E (2009)

Publication Type: Journal article

Publication year: 2009

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Book Volume: 41

Pages Range: 1508-1532

Journal Issue: 4

DOI: 10.1137/080731396

Abstract

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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Université Toulouse III - Paul Sabatier FR France (FR) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

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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