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Author Florian, Helmut
Title Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop : Proceedings of the International Graz Workshop
Imprint Singapore : World Scientific Publishing Company, 2001
©2001
book jacket
Descript 1 online resource (473 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Intro -- CONTENTS -- Preface -- 1 Boundary value problems and initial value problems for partial differential equations -- Hyperbolic equations, waves and the singularity theory -- On the regularity of solutions of the first boundary problem for higher order hyperbolic differential equations -- Zeilon's operator and lacunae -- Representation of the Stokes potential in divergence form -- On spectra of the operator rotor -- Algebraic properties of potential differential and pseudodifferential operators -- The method of weighted function spaces for solving initial value and boundary value problems -- The optimization of fixed-point methods -- Principle of Telethoscope -- Isometric mappings and the problem of A. D. Aleksandrov for conservative distances -- Natural metrics of differential equations (abstract) -- Embedding theorems in anisotropic functional spaces (abstract) -- Distributional analysis of boundary value problems in half-spaces-exemplifled by Melan's problem of elastostatics (abstract) -- Bäcklund transformations and nonlinear evolution equations (ABSTRACT) -- Nonlinear perturbations of systems of partial differential equations (ABSTRACT) -- Partial differential equations and cubature formulas (ABSTRACT) -- 2 Applications of functional-analytic and complex methods to mathematical physics -- Conservation laws for differential equations -- Applied quatemionic analysis. Maxwell's system and Dirac's equation -- Integral transforms method in the conjugation problems of electromagnetic fields -- Remarks on fundamental matrices (Green's Tensors) in elastodynamics, piezoelectricity and crystal optics -- Dynamical problems in the (0,0) and (1,0) approximations of a mathematical model of cusped bars -- Vanishing viscosity limit of the incompressible Navier-Stokes equation (ABSTRACT) -- 3 Partial complex differential equations in the plane
Boundary value problems for a class of nonregular elliptic equations -- On the solutions of the iterated Bers-Vekua equation -- The Bauer-Peschl equation - Derivation and solution of a partial differential equation by Laplace's method -- Komplexe Differenzengleichungen -- Stability of solutions of nonuniformly elliptic systems and boundary value problems -- An explicit solution to a class of second kind complex integral equation with singular and super-singular kernel -- An explicit solution to a class of second kind linear systems of complex integral equations with singular and super-singular kernels (abstract) -- Initial value problems for pseudoholomorphic functions (abstract) -- A boundary value problem for a special class of generalized analytic functions and its application to second order differential equations (abstract) -- Complex methods in operator theory (abstract) -- On one boundary value problem of the theory of analytic functions on a cut plane (abstract) -- 4 Complex methods in higher dimensions -- On a class of elliptic systems in the halfplane which are singular at the boundary -- Integral representations for inhomogeneous over-determined second order system of several complex equations -- Compactness of the canonical solution operator to ∂ restricted to Bergman spaces -- The theorem of the regular continuation for partial differential equations in general form and its applications -- Some higher order equations in Clifford analysis -- Generalizations of the complex analytic trigonometric functions to Clifford analysis by Eisenstein series -- Some implications of Clifford analysis (abstract) -- Around zeroes of monogenic and hypermonogenic functions (abstract) -- Identity surfaces
Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Florian, Helmut Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop : Proceedings of the International Graz Workshop Singapore : World Scientific Publishing Company,c2001 9789810247645
Subject Differential equations, Partial -- Congresses.;Functional analysis -- Congresses
Electronic books
Alt Author Ortner, Norbert
Schnitzer, Franz Josef
Tutschke, Wolfgang
Schnitzer, F.J
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