## On Dirichlet's Boundary Value Problem: LP-Theory based on a Generalization of Garding's Inequality |

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### Contents

A priori estimates for solutions of linear | 13 |

A representation for continuous linear functio | 84 |

Regularity and existence theorems for uniformly | 133 |

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Agmon Algebraic analogous apply arbitrary Assume assumptions of Theorem Bochner's theorem boundary dG boundary value problem bounded open set Category Theory coefficients completely continuous consider constant continuous linear functional continuous linear operator defined denotes derive dim N(T Dirichlet bilinear form Dirichlet problem Edited elliptic differential operators elliptic Dirichlet bilinear elliptic operator exists f e LP(G Fredholm's alternative holds Further G c Rn Garding's inequality Hilbert space Holder's inequality implies integer Koshelev Leibniz's rule Let G Let u e maps Math N(Tp N(Tq norm partial integration polynomial priori estimates proof of Theorem prove q. e. d. Theorem real numbers regular Dirichlet bilinear regularity theorems Rellich's theorem representation S.Agmon satisfied Seiten Seminar set with boundary Sobolev Theorem 1.6 Theory trivial uniformly elliptic Dirichlet uniformly strongly elliptic x e G