Observability inequalities and measurable sets

Apraiz, 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 -