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Locations of interior transition layers to inhomogeneous transition problems in higher -dimensional domains
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 3 / June 2023
- Published online by Cambridge University Press:
- 08 March 2022, pp. 764-783
- Print publication:
- June 2023
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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.
