Download E-books Partial Differential Equations in Several Complex Variables PDF

This ebook is meant either as an introductory textual content and as a reference e-book for these attracted to learning a number of advanced variables within the context of partial differential equations. within the previous couple of a long time, major development has been made within the fields of Cauchy-Riemann and tangential Cauchy-Riemann operators. This booklet supplies an updated account of the theories for those equations and their purposes. The heritage fabric in different advanced variables is built within the first 3 chapters, resulting in the Levi challenge. the following 3 chapters are dedicated to the solvability and regularity of the Cauchy-Riemann equations utilizing Hilbert house techniques.The authors supply a scientific learn of the Cauchy-Riemann equations and the $\bar\partial$-Neumann challenge, together with $L^2$ life theorems on pseudoconvex domain names, $\frac 12$-subelliptic estimates for the $\bar\partial$-Neumann difficulties on strongly pseudoconvex domain names, worldwide regularity of $\bar\partial$ on extra common pseudoconvex domain names, boundary regularity of biholomorphic mappings, irregularity of the Bergman projection on malicious program domain names. the second one a part of the publication provides a accomplished examine of the tangential Cauchy-Riemann equations. bankruptcy 7 introduces the tangential Cauchy-Riemann advanced and the Lewy equation. an in depth account of the $L^2$ thought for $\square_b$ and $\bar\partial_b$ is given in Chapters eight and nine. specific imperative resolution representations are built either at the Heisenberg teams and on strictly convex limitations with estimates in Ho$lder and $L^p$ spaces.Embeddability of summary $CR$ buildings is mentioned intimately within the final bankruptcy. This self-contained booklet offers a much-needed introductory textual content to a number of complicated variables and partial differential equations. it's also a wealthy resource of data to specialists.

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