Holder estimates for the $\bar\partial$-equation on surfaces with simple singularities
Holder estimates for the $\bar\partial$-equation on surfaces with simple singularities
Let $��$ 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 $��$, demanding a Holder condition on the solution.
11 pages
32F20, 32W05, 35N15, Mathematics - Analysis of PDEs, \(\bar\partial\)-operator, Mathematics - Complex Variables, FOS: Mathematics, spaces with singularity, Hölder solutions, Complex Variables (math.CV), \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Analysis of PDEs (math.AP)
32F20, 32W05, 35N15, Mathematics - Analysis of PDEs, \(\bar\partial\)-operator, Mathematics - Complex Variables, FOS: Mathematics, spaces with singularity, Hölder solutions, Complex Variables (math.CV), \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Analysis of PDEs (math.AP)
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