The Hodge-Laplacian : boundary value problems on Riemannian manifolds / Dorina Mitrea [and three others].

Format:

Book

Author/Creator:

Mitrea, Dorina, author.

Mitrea, Dorina, 1965- author.

Series:

De Gruyter studies in mathematics ; Volume 64.

De Gruyter Studies in Mathematics, 0179-0986 ; Volume 64

Language:

English

Subjects (All):

Riemannian manifolds.

Boundary value problems.

Physical Description:

1 online resource (528 pages).

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2016.

Language Note:

In English.

Summary:

The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains.Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents:PrefaceIntroduction and Statement of Main ResultsGeometric Concepts and ToolsHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR DomainsHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR DomainsDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT DomainsFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT DomainsSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham FormalismAdditional Results and ApplicationsFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford AnalysisBibliographyIndex

Contents:

Frontmatter

Preface

Contents

1. Introduction and Statement of Main Results

2. Geometric Concepts and Tools

3. Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains

4. Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains

5. Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains

6. Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains

7. Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism

8. Additional Results and Applications

9. Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis

Bibliography

Index

Backmatter

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9783110483390

3110483394

9783110484380

3110484382

OCLC:

960041744