Bulletin of the Korean Mathematical Society (대한수학회보)

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

  • Received : 2020.06.30
  • Accepted : 2021.01.14
  • Published : 2021.05.31
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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 ${\frac{1}{\eta}}$.

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References

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