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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 fixedpoint 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 halfspacesexemplifled 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 functionalanalytic 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 NavierStokes 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 BersVekua equation  The BauerPeschl 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 supersingular kernel  An explicit solution to a class of second kind linear systems of complex integral equations with singular and supersingular 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 overdetermined 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 FunctionalAnalytic 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 Functionalanalytic 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

