## A finite element method for the Tricomi problem in the elliptic region |

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### Contents

Weighted Sobolev Spaces | 5 |

Bounds for Piecewise Polynomial Approximation | 33 |

Abels Integral Operator | 53 |

4 other sections not shown

### Common terms and phrases

1+CP Abel's inversion formula Agmon apply Bitsadze bounded linear operator bounded sublinear functional Cauchy data Cauchy sequences completes the lemma converges in H converges uniformly Cornell University Corollary 3.5 define denote derive dt dx dx dt elliptic problem elliptic region elliptic subproblem equation exists a constant Fh(uh finite difference method finite element method Hence by Corollary Hermite Interpolation Hilbert Hk(G hx,hy hyperbolic problem inclusion map JBjJbi Lax-Milgram Lax-Milgram theorem limits of Cauchy linear subspace maximum principle non-local boundary condition order of integration polynomials prove a version rate of convergence Rellich lemma result satisfies the hypotheses Schwartz's inequality Sobolev's inequality solution subsequence subspace Suppose Theorem 2.3 trace inequality Tricomi problem u e Hk unique usual Sobolev Uxuxy UxUyy Vy dx dy weighted Sobolev spaces weighted spaces zero