A bound on H\"older regularity for $\overline \partial$-equation on pseudoconvex domains in $\mathbb C^n$ with some comparable eigenvalues of the Levi-form

Abstract : \noindent Let $\Omega $ be a smoothly bounded pseudoconvex domain in $\cn $ and assume that the $(n-2)$-eigenvalues of the Levi-form are comparable in a neighborhood of $z_0\in \bo$. Also, assume that there is a smooth 1-dimensional analytic variety $V$ whose order of contact with $\bo$ at $z_0$ is equal to $\eta$ and $\Delta_{n-2}(z_0)<\infty$. We show that the maximal gain in H\"older regularity for solutions of the $\dbar$-equation is at most $\frac {1}{\eta}$.

Keywords : H\"older estimates of $\dbar$, finite type, comparable Levi-forms