## 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

Contents PHYS | 1 |

INTEGRAL OPERATORS FOR ELLIPTIC EQUATIONS | 36 |

ANALYTIC CONTINUATION | 57 |

Copyright | |

2 other sections not shown

### Common terms and phrases

absolutely and uniformly adjoint equation analytic continuation analytic function arbitrary boundary value problem bounded Cauchy data Cauchy's coefficients compact subset complete family complex variables Consider construct convex Corollary cose defined ecº elliptic Cauchy problem elliptic equations entire function envelope method equa Exercise exists exponential type family of solutions figure fundamental solution Green's formula Helmholtz equation Hence implies improperly posed initial value problem integral operators inverse Lemma Let u(x neighbourhood Note orem origin P2 f parabolic partial differential equation partially analytic plane polynomial Proof Pseudoparabolic Equations radiation pattern regular solution Riemann function Runge approximation property ſ ſ simply connected domain singularities ſº solution of 9.1 solution of Lu solution of Mwo solutions of equation Sommerfeld radiation condition Stefan problem ſul Suppose surface Theorem 16 Theorem F tion uniformly and absolutely uniquely determined