Original scientific paper

A priori estimates for finite-energy sequences of Muller's functional with non-coercive two-well potential with symmetrically placed wells

Andrija Raguž orcid.org/0000-0001-8045-9636 ; Department of Mathematics and Statistics, Zagreb School of Economics and Management, Zagreb

Abstract

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 $\int_{-\infty}^{0}\sqrt{W}=\int_{0}^{+\infty}\sqrt{W}=+\infty$.

Keywords

Asymptotic analysis; singular perturbation; Young measures; Modica-Mortola functional; Gamma convergence

Hrčak ID:

215149

URI

https://hrcak.srce.hr/215149

Publication date:

19.4.2019.

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