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We investigate the Allen-Cahn system  \begin{equation*}  \Delta u-W_u(u)=0,\quad u:\mathbb{R}^2\rightarrow\mathbb{R}^2,  \end{equation*}  where $W\in C^2(\mathbb{R}^2,[0,+\infty))$ is a potential with three globalminima. We establish the existence of an entire solution $u$ which possesses atriple junction structure. The main strategy is to study the global minimizer$u_\varepsilon$ of the variational problem  \begin{equation*}  \min\int_{B_1} \left( \frac{\varepsilon}{2}|\nablau|^2+\frac{1}{\varepsilon}W(u) \right)\,dz,\ \ u=g_\varepsilon \text{ on}\partial B_1.  \end{equation*}  The point of departure is an energy lower bound that plays a crucial role inestimating the location and size of the diffuse interface. We do not impose anysymmetry hypothesis on the solution.

On the triple junction problem on the plane without symmetry hypotheses