Holder estimates for the $\bar\partial$-equation on surfaces with simple singularities

Let $\Sigma$ be a 2-dimensional subvariety in $C^3$ with an isolated simple (rational double point) singularity at the origin. The main objective of this paper is to solve the $\dbar$-equation on a neighbourhood of the origin in $\Sigma$, demanding a Holder condition on the solution.

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Bibliographic Details
Main Authors Acosta, F, Zeron, E. S
Format Journal Article
LanguageEnglish
Published 20.07.2006
Subjects
Mathematics - Analysis of PDEs
Mathematics - Complex Variables
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Summary:Let $\Sigma$ be a 2-dimensional subvariety in $C^3$ with an isolated simple (rational double point) singularity at the origin. The main objective of this paper is to solve the $\dbar$-equation on a neighbourhood of the origin in $\Sigma$, demanding a Holder condition on the solution.
DOI:10.48550/arxiv.math/0607502