In this paper we obtain a priori estimates for finite-energy sequences of M\"uller's functional $$I^{\varepsilon}_a(v)=\int_{0}^{1}\Big({\varepsilon}^2v''^2(s)+W(v'(s))+a(s)v^2(s)\Big)ds\;,$$ where $v\in {\rm H}^{2}\oi{0}{1}$ and $W$ is non-coercive two-well potential with symmetrically placed zero-points. We prove $\Gamma$-convergence of corresponding relaxed functionals accordingto the approach of G. Alberti and S. M\"uller as $\varepsilon\longrightarrow 0$ for $W$ which satisfies $\int_{-\infty}^{0}\sqrt{W}=\int_{0}^{+\infty}\sqrt{W}=+\infty$.
Publié le : 2018-12-05
Classification:
Asymptotic analysis, singular perturbation, Young measures, Modica-Mortola functional, Gamma convergence,
34E15, 49J45
@article{mc2298,
author = {Ragu\v z, Andrija},
title = {A priori estimates for finite-energy sequences of Muller's functional with non-coercive two-well potential with symmetrically placed wells},
journal = {Mathematical Communications},
volume = {23},
number = {2},
year = {2018},
pages = { 39-59},
language = {eng},
url = {http://dml.mathdoc.fr/item/mc2298}
}
Raguž, Andrija. A priori estimates for finite-energy sequences of Muller's functional with non-coercive two-well potential with symmetrically placed wells. Mathematical Communications, Tome 23 (2018) no. 2, pp. 39-59. http://gdmltest.u-ga.fr/item/mc2298/