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http://dx.doi.org/10.4134/BKMS.b200569

A BOUND ON HÖLDER REGULARITY FOR ${\bar{\partial}}$-EQUATION ON PSEUDOCONVEX DOMAINS IN ℂn WITH SOME COMPARABLE EIGENVALUES OF THE LEVI-FORM  

Cho, Sanghyun (Department of Mathematics Sogang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.3, 2021 , pp. 781-794 More about this Journal
Abstract
Let Ω 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 z0 ∈ bΩ. Also, assume that there is a smooth 1-dimensional analytic variety V whose order of contact with bΩ at z0 is equal to 𝜂 and 𝚫n-2(z0) < ∞. We show that the maximal gain in Hölder regularity for solutions of the ${\bar{\partial}}$-equation is at most ${\frac{1}{\eta}}$.
Keywords
$H{\ddot{o}}lder$ estimates of ${\bar{\partial}}$; finite type; comparable Levi-forms;
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