Estimates for the ∂¯ -Equation on Canonical Surfaces
Journal article, 2020

We study the solvability in Lp of the ∂¯ -equation in a neighborhood of a canonical singularity on a complex surface, a so-called du Val singularity. We get a quite complete picture in case p= 2 for two natural closed extensions ∂¯ s and ∂¯ w of ∂¯. For ∂¯ s we have solvability, whereas for ∂¯ w there is solvability if and only if a certain boundary condition (∗) is fulfilled at the singularity. Our main tool is certain integral operators for solving ∂¯ introduced by the first and fourth author, and we study mapping properties of these operators at the singularity.

Canonical surface

Koppelman formulas

L -estimates p

Cauchy–Riemann equations

Singular complex spaces

Author

Mats Andersson

Chalmers, Mathematical Sciences, Algebra and geometry

Richard Lärkäng

Chalmers, Mathematical Sciences, Algebra and geometry

Jean Ruppenthal

Bergische Universität Wuppertal

Håkan Samuelsson

Chalmers, Mathematical Sciences, Algebra and geometry

Elizabeth Wulcan

Chalmers, Mathematical Sciences, Algebra and geometry

Journal of Geometric Analysis

1050-6926 (ISSN)

Vol. 30 3 2974-3001

Subject Categories

Computational Mathematics

Geometry

Mathematical Analysis

DOI

10.1007/s12220-019-00187-2

More information

Latest update

9/16/2020