Obstructions to uniform estimates for solutions to the d-bar equation

Gautam Bharali

Obstructions to uniform estimates for solutions to the d-bar equation

Complex Variables 2009-03-26 v2 Analysis of PDEs

Authors: Gautam Bharali

Abstract

We show that if, for every bounded d-bar-closed (0,1)-form f, a pseudoconvex domain \Omega admits a solution to $\bar\partial u=f$ that is continuous up to the boundary and has uniform estimates in terms of $\|f\|_\infty$ , then each p\in bdy(\Omega) must necessarily admit a peak function in the class $A(\Omega):=\mathcal{O}(\Omega)\cap\mathcal{C}(\overline\OM)$ . We use this fact to examine some geometrical obstructions to uniform estimates for the d-bar equation.

Keywords

d-bar equation uniform estimates pseudoconvex domain peak function geometric obstruction boundary regularity

Cite

@article{arxiv.0903.3908,
  title  = {Obstructions to uniform estimates for solutions to the d-bar equation},
  author = {Gautam Bharali},
  journal= {arXiv preprint arXiv:0903.3908},
  year   = {2009}
}

Comments

This preprint has been withdrawn by the author because the estimate (2.3) does not follow from the formula preceding it

Obstructions to uniform estimates for solutions to the d-bar equation

Abstract

Keywords

Cite

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