About stability of equilibrium shapes
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 34, Issue: 4, page 811-834
- ISSN: 0764-583X
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topDambrine, Marc, and Pierre, Michel. "About stability of equilibrium shapes." ESAIM: Mathematical Modelling and Numerical Analysis 34.4 (2010): 811-834. <http://eudml.org/doc/197610>.
@article{Dambrine2010,
abstract = {
We discuss the stability of "critical" or "equilibrium" shapes of
a shape-dependent energy functional. We analyze a problem arising when
looking at the positivity of the second derivative in order to prove
that a critical shape is an optimal shape. Indeed, often when
positivity -or coercivity- holds, it does for a weaker norm than the
norm for which the functional is twice differentiable and local
optimality cannot be a priori deduced. We solve this problem for a
particular but significant example. We prove "weak-coercivity" of
the second derivative uniformly in a "strong" neighborhood of the
equilibrium shape.
},
author = {Dambrine, Marc, Pierre, Michel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Shape optimisation; stability of critical shape; weak coercivity;
area-preserving transformations.; shape-dependent energy functional; critical shape; optimal shape},
language = {eng},
month = {3},
number = {4},
pages = {811-834},
publisher = {EDP Sciences},
title = {About stability of equilibrium shapes},
url = {http://eudml.org/doc/197610},
volume = {34},
year = {2010},
}
TY - JOUR
AU - Dambrine, Marc
AU - Pierre, Michel
TI - About stability of equilibrium shapes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 4
SP - 811
EP - 834
AB -
We discuss the stability of "critical" or "equilibrium" shapes of
a shape-dependent energy functional. We analyze a problem arising when
looking at the positivity of the second derivative in order to prove
that a critical shape is an optimal shape. Indeed, often when
positivity -or coercivity- holds, it does for a weaker norm than the
norm for which the functional is twice differentiable and local
optimality cannot be a priori deduced. We solve this problem for a
particular but significant example. We prove "weak-coercivity" of
the second derivative uniformly in a "strong" neighborhood of the
equilibrium shape.
LA - eng
KW - Shape optimisation; stability of critical shape; weak coercivity;
area-preserving transformations.; shape-dependent energy functional; critical shape; optimal shape
UR - http://eudml.org/doc/197610
ER -
References
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