Partial differential equations and complex analysis. (English) Zbl 0852.35001

Studies in Advanced Mathematics. Boca Raton, FL: CRC Press. xii, 297 p. (1992).
Publisher’s description: The book is an excellent introduction to linear partial differential equations, Fourier analysis, pseudodifferential operators, elliptic boundary value problems, theory of the \(\overline\partial\)-Neumann problem, and question of local solvability. Many of the issues considered appear here in book form for the first time.
Contents: The Dirichlet Problem in the Complex Plane. Review of Fourier Analysis. Pseudodifferential Operators. Elliptic Operators. Elliptic Boundary Value Problems. A Degenerate Elliptic Boundary Value Problem. The \(\overline\partial\)-Neumann Problem. Applications of the \(\overline\partial\)-Neumann Problem. The Local Solvability Issue and a Look Back.


35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
32Fxx Geometric convexity in several complex variables