Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem

Released on by Emil J. Straube
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  • Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem Book Detail

  • Author : Emil J. Straube
  • Release Date : 2010
  • Publisher : European Mathematical Society
  • Genre : Mathematics
  • Pages : 220
  • ISBN 13 : 9783037190760
  • File Size : 68,68 MB
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Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem by Emil J. Straube PDF Summary

Book Description: This book provides a thorough and self-contained introduction to the $\bar{\partial}$-Neumann problem, leading up to current research, in the context of the $\mathcal{L}^{2}$-Sobolev theory on bounded pseudoconvex domains in $\mathbb{C}^{n}$. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrodinger International Institute for Mathematical Physics and at Texas A & M University. The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic $\mathcal{L}^{2}$-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research. Prerequisites are a solid background in basic complex and functional analysis, including the elementary $\mathcal{L}^{2}$-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.

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Handbook of Complex Analysis

Handbook of Complex Analysis

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In spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications