<p>Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions and generalized regular functions in real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, the definitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by Luogeng Hua for complex analysis of several variables. The great majority of the contents originate in the authors’ investigations, and this new monograph will be interesting for researchers studying the theory of functions.</p>

Real and Complex Clifford Analysis (Advances in Complex Analysis and Its Applications, 5)

Science & Math

Huang, Sha

Qiao, Yu Ying

Wen, Guo-Chun

Mathematics

Springer

This text uses complex and functional analytic methods to treat boundary value problems for non-linear equations and systems of first and higher order in multiply-connected plane domains. Also presented are applications in continuum mechanics.

Nonlinear Elliptic Boundary Value Problems and Their Applications (Monographs and Surveys in Pure and Applied Mathematics)

Begehr, H

Chapman and Hall/CRC

Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions and generalized regular functions in real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, the definitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by Luogeng Hua for complex analysis of several variables. The great majority of the contents originate in the authors’ investigations, and this new monograph will be interesting for researchers studying the theory of functions.

<p>This book deals mainly with linear and nonlinear parabolic equations and systems of second order. It first transforms the real forms of parabolic equations and systems into complex forms, and then discusses several initial boundary value problems and Cauchy problems for quasilinear and nonlinear parabolic complex equations of second order with smooth coefficients or measurable coefficients. Parabolic complex equations are discussed in the nonlinear case and the boundary conditions usually include the initial irregular oblique derivative. The boundary value problems are considered in multiply connected domains and several methods are used.</p>

LINEAR AND NONLINEAR PARABOLIC COMPLEX EQUATIONS

World Scientific Pub Co Inc

In the recent half-century, many mathematicians have investigated various problems on several equations of mixed type and obtained interesting results, with important applications to gas dynamics. However, the Tricomi problem of general mixed type equations of second order with parabolic degeneracy has not been completely solved, particularly the Tricomi and Frankl problems for general Chaplygin equation in multiply connected domains posed by L Bers, and the existence, regularity of solutions of the above problems for mixed equations with non-smooth degenerate curve in several domains posed by J M Rassias.The method revealed in this book is unlike any other, in which the hyperbolic number and hyperbolic complex function in hyperbolic domains, and the complex number and complex function in elliptic domains are used. The corresponding problems for first order complex equations with singular coefficients are first discussed, and then the problems for second order complex equations are considered, where we pose the new partial derivative notations and complex analytic methods such that the forms of the above first order complex equations in hyperbolic and elliptic domains are wholly identical. In the meantime, the estimates of solutions for the above problems are obtained, hence many open problems including the above Tricomi- Bers and Tricomi-Frankl-Rassias problems can be solved.

Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy: Including Tricomi-Bers and Tricomi-Frankl-Rrassias Problems (Peking University Series in Mathematics)

World Scientific Publishing Company

See the best price to sell, buy, or rent books by Wen, Guo-Chun. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Wen, Guo-Chun

See the best price to sell, buy, or rent books by Wen, Guo-Chun. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Real and Complex Clifford Analysis (Advances in Complex Analysis and Its Applications, 5)

Nonlinear Elliptic Boundary Value Problems and Their Applications (Monographs and Surveys in Pure and Applied Mathematics)

Real and Complex Clifford Analysis (Advances in Complex Analysis and Its Applications, 5)

LINEAR AND NONLINEAR PARABOLIC COMPLEX EQUATIONS

Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy: Including Tricomi-Bers and Tricomi-Frankl-Rrassias Problems (Peking University Series in Mathematics)