Abstract
We consider the following inhomogeneous problems
\[ \begin{cases} \epsilon^{2}\mbox{div}(a(x)\nabla u(x))+f(x,u)=0 & \text{ in }\Omega,\\ \frac{\partial u}{\partial \nu}=0 & \text{ on }\partial \Omega,\\ \end{cases} \]
where
$\Omega$
is a smooth and bounded domain in general dimensional space
$\mathbb {R}^{N}$
,
$\epsilon >0$
is a small parameter and function
$a$
is positive. We respectively obtain the locations of interior transition layers of the solutions of the above transition problems that are
$L^{1}$
-local minimizer and global minimizer of the associated energy functional.
Publisher
Cambridge University Press (CUP)
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