Estimates for the ∂¯ -Equation on Canonical Surfaces
Artikel i vetenskaplig tidskrift, 2019

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.

Singular complex spaces

L -estimates p

Canonical surface

Cauchy–Riemann equations

Koppelman formulas

Författare

Mats Andersson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Richard Lärkäng

Chalmers, Matematiska vetenskaper, Algebra och geometri

Jean Ruppenthal

Bergische Universität Wuppertal

Håkan Samuelsson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Elizabeth Wulcan

Chalmers, Matematiska vetenskaper, Algebra och geometri

Journal of Geometric Analysis

1050-6926 (ISSN)

Vol. In Press

Ämneskategorier

Beräkningsmatematik

Geometri

Matematisk analys

DOI

10.1007/s12220-019-00187-2

Mer information

Senast uppdaterat

2020-03-25