Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds / [electronic resource] Dorina Mitrea, Marius Mitrea, Michael Taylor.

By: Mitrea, Dorina, 1965-Contributor(s): Mitrea, Marius | Taylor, MichaelMaterial type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 713Publication details: Providence, R.I. : American Mathematical Society, 2001Description: 1 online resource (viii, 120 p.)ISBN: 9781470403065 (online)Subject(s): Riemannian manifolds | Boundary value problems | Differential equations, Elliptic -- Numerical solutionsAdditional physical formats: Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds /DDC classification: 510 s | 516.3/73 LOC classification: QA3 | .A57 no. 713 | QA649Online resources: Contents | Contents
Contents:
Introduction 1. Singular integrals on Lipschitz submanifolds of codimension one 2. Estimates on fundamental solutions 3. General second-order strongly elliptic systems 4. The Dirichlet problem for the Hodge Laplacian and related operators 5. Natural boundary problems for the Hodge Laplacian in Lipschitz domains 6. Layer potential operators on Lipschitz domains 7. Rellich type estimates for differential forms 8. Fredholm properties of boundary integral operators on regular spaces 9. Weak extensions of boundary derivative operators 10. Localization arguments and the end of the proof of Theorem 6.2 11. Harmonic fields on Lipschitz domains 12. The proofs of the Theorems 5.1-5.5 13. The proofs of the auxiliary lemmas 14. Applications to Maxwell's equations on Lipschitz domains
Item type: E-BOOKS
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Link to resource Available EBK13166

"Volume 150, number 713 (fourth of 5 numbers)."

Includes bibliographical references (p. 117-120).

Introduction 1. Singular integrals on Lipschitz submanifolds of codimension one 2. Estimates on fundamental solutions 3. General second-order strongly elliptic systems 4. The Dirichlet problem for the Hodge Laplacian and related operators 5. Natural boundary problems for the Hodge Laplacian in Lipschitz domains 6. Layer potential operators on Lipschitz domains 7. Rellich type estimates for differential forms 8. Fredholm properties of boundary integral operators on regular spaces 9. Weak extensions of boundary derivative operators 10. Localization arguments and the end of the proof of Theorem 6.2 11. Harmonic fields on Lipschitz domains 12. The proofs of the Theorems 5.1-5.5 13. The proofs of the auxiliary lemmas 14. Applications to Maxwell's equations on Lipschitz domains

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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