Higher-order partial differential equations in Clifford analysis. Effective solutions to problems
type: Item
instance of: scholarly article
title: Higher-order partial differential equations in Clifford analysis. Effective solutions to problems
zbMATH Open document ID: 1038.30022
author: Elena Obolashvili
published in: Progress in Mathematical Physics
publication date: 2003-02-02T00:00:00Z
review text: Boundary value problems (BVP) and initial -BVP for systems of PDE for canonical domains are solved in the book. One of the typical equations has the form \(( \Delta -\frac{\partial ^{2}}{\partial t^{2}}) ( \Delta -\frac{\partial }{\partial \tau } u(x,t,\tau )=0\). The solutions of the problems has been obtained in closed form. The book contains many interesting formulas for solutions of BVP, mainly for the half-space. The author does not cite [\textit{È. I. Zverovich}, Russ. Math. Surv. 26 (1971), No. 1, 117--192 (1972); translation from Usp. Mat. Nauk 26, No.1(157), 113--179 (1971; Zbl 0217.10201)] and [\textit{V. V. Mityushev} and \textit{S. V. Rogosin}, Constructive methods for linear and nonlinear boundary value problems for analytic functions: theory and applications (2000; Zbl 0957.30002)], where some problems for harmonic and biharmonic functions are solved in more general statements. Contents of the book: Part I. BVP for regular, generalized regular and pluriregular elliptic equations. 1. Two-dimensional case. BVP for classical and generalized Beltrami equations, for plurigeneralized holomorphic, polyharmonic, polymetaharmonic functions etc. are solved. 2. Multidimensional cases. Elements of Clifford analysis are presented. BVP for poly-Helmholtz, pluri-Beltrami equations etc. in Clifford analysis are solved. Part II. Initial value problems for regular and pluriregular hyperbolic and parabolic equations. 3. Hyperbolic and plurihyperbolic equations in Clifford analysis. 4. Parabolic and pluriparabolic equations in Clifford analysis.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 30-02
Mathematics Subject Classification ID: 35G05
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 31-02
zbMATH DE Number: 1862426
zbMATH Keywords: Clifford analysis
zbMATH Keywords: boundary value problem
zbMATH Keywords: Beltrami equation
zbMATH Keywords: polyharmonic function
zbMATH Keywords: polymetaharmonic function
zbMATH Keywords: pluriholomorphic function
zbMATH Keywords: elliptic-hyperbolic-parabolic equation
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1862426