# Observability inequalities and measurable sets

Jone Apraiz; Luis Escauriaza; Gengsheng Wang; C. Zhang

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 11, page 2433-2475
- ISSN: 1435-9855

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topApraiz, Jone, et al. "Observability inequalities and measurable sets." Journal of the European Mathematical Society 016.11 (2014): 2433-2475. <http://eudml.org/doc/277551>.

@article{Apraiz2014,

abstract = {This paper presents two observability inequalities for the heat equation over $\Omega \times (0,T)$. In the first one, the observation is from a subset of positive measure in $\Omega \times (0,T)$, while in the second, the observation is from a subset of positive surface measure on $\partial \Omega \times (0,T)$. It also proves the Lebeau-Robbiano spectral inequality when $\Omega $ is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.},

author = {Apraiz, Jone, Escauriaza, Luis, Wang, Gengsheng, Zhang, C.},

journal = {Journal of the European Mathematical Society},

keywords = {observability inequality; heat equation; measurable set; spectral inequality; observability inequality; heat equation; measurable set; spectral inequality},

language = {eng},

number = {11},

pages = {2433-2475},

publisher = {European Mathematical Society Publishing House},

title = {Observability inequalities and measurable sets},

url = {http://eudml.org/doc/277551},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Apraiz, Jone

AU - Escauriaza, Luis

AU - Wang, Gengsheng

AU - Zhang, C.

TI - Observability inequalities and measurable sets

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 11

SP - 2433

EP - 2475

AB - This paper presents two observability inequalities for the heat equation over $\Omega \times (0,T)$. In the first one, the observation is from a subset of positive measure in $\Omega \times (0,T)$, while in the second, the observation is from a subset of positive surface measure on $\partial \Omega \times (0,T)$. It also proves the Lebeau-Robbiano spectral inequality when $\Omega $ is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.

LA - eng

KW - observability inequality; heat equation; measurable set; spectral inequality; observability inequality; heat equation; measurable set; spectral inequality

UR - http://eudml.org/doc/277551

ER -

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