# Does Max Planar 3-SAT admit a PTAS?

Suppose we are given a formula $$\phi$$ of 3-SAT, with variables $$x_1,\dots, x_n$$ and clauses $$C_1,\dots, C_m$$. Consider the graph $$G_\phi$$ where there is one node for each clause $$C_i$$, for each positive literal $$x_i$$ and for each negative literal $$\overline{x_i}$$. A literal is adjacent to a clause if and only if this clause contains the literal. $$\phi$$ is a planar instance If $$G_\phi$$ is planar.

Max planar 3-SAT is defined as the restriction of Max 3-SAT to planar instances.

This problem is known to be NP-hard. Is this problem also APX-Hard or there exists a known PTAS for this problem ?