## Partial differential equations in the complex domainImproperly posed initial value problems; Integral operators for elliptic equations; Analytic continuation; Pseudoparabilic equations. |

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### Contents

INTRODUCTION | |

IMPROPERLY POSED INITIAL VALUE PROBLEMS | ii |

INTEGRAL OPERATORS FOR ELLIPTIC EQUATIONS | 36 |

Copyright | |

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### Common terms and phrases

absolutely and uniformly analytic continuation arbitrary assume Axially Symmetric Helmholtz boundary value problem Cauchy's coefficients compact subset complete family complex variables conformal mapping construct convex cos9 D U a U D defined elliptic Cauchy problem elliptic equations entire function envelope method equa Exercise exponential type family of solutions figure fundamental solution G U G Goursat problems Green's formula Hence implies improperly posed indicator diagram initial value problem integral operators inverse Lemma mapping analytic functions neighbourhood Note operators for elliptic origin partial differential equation partially analytic plane polynomial Proof Pseudoparabolic Equations radiation condition radiation pattern regular solution Riemann function Runge approximation property simply connected domain singularities solution of 9.1 solution of Lu solutions of equation Sommerfeld radiation Sommerfeld radiation condition Stefan problem Suppose surface Symmetric Helmholtz Equation Theorem F tion uniformly and absolutely uniquely determined