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Partial Differential Equations 1

Foundations and Integral Representations

  • Friedrich Sauvigny

Part of the Universitext book series (UTX)

About this book

Introduction

This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put on the connection of PDEs and complex variable methods.

In this first volume the following topics are treated: Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potential theory and spherical harmonics, Linear partial differential equations. While we solve the partial differential equations via integral representations in this volume, we shall present functional analytic solution methods in the second volume.

This textbook can be chosen for a course over several semesters on a medium level. Advanced readers may study each chapter independently from the others.

Keywords

Differential Geometry Partial Differential Equations Potential Potential Theory functional analysis partial differential equation

Authors and affiliations

  • Friedrich Sauvigny
    • 1
  1. 1.Lehrstuhl Mathematik, insbes. AnalysisBrandenburgische Technische Universität Cottbus Fakultät 1CottbusGermany

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