## Lecture Series of the Symposium on Partial Differential Equations: Held at the University of California, at Berkeley, June 20-July 1, 1955 |

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### Contents

ON NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS | 1 |

DIFFERENCE APPROXIMATION TO SOLUTIONS OF LINEAR | 33 |

A PHRAGMENLINDELOF PRINCIPLE IN HARMONIC | 67 |

Copyright | |

1 other sections not shown

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algebra An(h analytic function applied approximation scheme assumed boundary condition boundary points boundary value problems compact space completely continuous considered const constant coefficients convergence curve defined denote depends difference operators differential equation 2.1 Dirichlet integral domain easily eigenfunctions eigenvalue electrostatic element elliptic equations elliptic operator equal estimate exists exponential finite Dirichlet fixed fluid follows Fourier coefficients function f given Green's formula Green's function Green's identity harmonic function Hence holds hydrodynamical identity independent inequality infinity interior compact space interval Laplace's equation Lemma linear Lipschitz continuous Math method metric Neumann's condition norm normal derivative obtained parameter partial differential equation particular solutions principle prove respect satisfies scalar selfadjoint solution of Lu spectral radius sphere stability Suppose surface symmetric tends to zero theorem theory tion translation invariant translation operator uniformly bounded University vanishes variational formulas vector zero Dirichlet data