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Sets of Finite Perimeter and Geometric Variational Problems
Buch von Francesco Maggi
Sprache: Englisch

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Beschreibung
An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.
An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.
Über den Autor
Francesco Maggi is an Associate Professor at the University of Texas, Austin, USA.
Inhaltsverzeichnis
Part I. Radon Measures on Rn: 1. Outer measures; 2. Borel and Radon measures; 3. Hausdorff measures; 4. Radon measures and continuous functions; 5. Differentiation of Radon measures; 6. Two further applications of differentiation theory; 7. Lipschitz functions; 8. Area formula; 9. Gauss-Green theorem; 10. Rectifiable sets and blow-ups of Radon measures; 11. Tangential differentiability and the area formula; Part II. Sets of Finite Perimeter: 12. Sets of finite perimeter and the Direct Method; 13. The coarea formula and the approximation theorem; 14. The Euclidean isoperimetric problem; 15. Reduced boundary and De Giorgi's structure theorem; 16. Federer's theorem and comparison sets; 17. First and second variation of perimeter; 18. Slicing boundaries of sets of finite perimeter; 19. Equilibrium shapes of liquids and sessile drops; 20. Anisotropic surface energies; Part III. Regularity Theory and Analysis of Singularities: 21. (¿, r0)-perimeter minimizers; 22. Excess and the height bound; 23. The Lipschitz approximation theorem; 24. The reverse Poincaré inequality; 25. Harmonic approximation and excess improvement; 26. Iteration, partial regularity, and singular sets; 27. Higher regularity theorems; 28. Analysis of singularities; Part IV. Minimizing Clusters: 29. Existence of minimizing clusters; 30. Regularity of minimizing clusters; References; Index.
Details
Erscheinungsjahr: 2016
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 476
Inhalt: Gebunden
ISBN-13: 9781107021037
ISBN-10: 1107021030
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Maggi, Francesco
Hersteller: Cambridge University Press
Maße: 235 x 157 x 32 mm
Von/Mit: Francesco Maggi
Erscheinungsdatum: 03.08.2016
Gewicht: 0,919 kg
preigu-id: 106438158
Über den Autor
Francesco Maggi is an Associate Professor at the University of Texas, Austin, USA.
Inhaltsverzeichnis
Part I. Radon Measures on Rn: 1. Outer measures; 2. Borel and Radon measures; 3. Hausdorff measures; 4. Radon measures and continuous functions; 5. Differentiation of Radon measures; 6. Two further applications of differentiation theory; 7. Lipschitz functions; 8. Area formula; 9. Gauss-Green theorem; 10. Rectifiable sets and blow-ups of Radon measures; 11. Tangential differentiability and the area formula; Part II. Sets of Finite Perimeter: 12. Sets of finite perimeter and the Direct Method; 13. The coarea formula and the approximation theorem; 14. The Euclidean isoperimetric problem; 15. Reduced boundary and De Giorgi's structure theorem; 16. Federer's theorem and comparison sets; 17. First and second variation of perimeter; 18. Slicing boundaries of sets of finite perimeter; 19. Equilibrium shapes of liquids and sessile drops; 20. Anisotropic surface energies; Part III. Regularity Theory and Analysis of Singularities: 21. (¿, r0)-perimeter minimizers; 22. Excess and the height bound; 23. The Lipschitz approximation theorem; 24. The reverse Poincaré inequality; 25. Harmonic approximation and excess improvement; 26. Iteration, partial regularity, and singular sets; 27. Higher regularity theorems; 28. Analysis of singularities; Part IV. Minimizing Clusters: 29. Existence of minimizing clusters; 30. Regularity of minimizing clusters; References; Index.
Details
Erscheinungsjahr: 2016
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 476
Inhalt: Gebunden
ISBN-13: 9781107021037
ISBN-10: 1107021030
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Maggi, Francesco
Hersteller: Cambridge University Press
Maße: 235 x 157 x 32 mm
Von/Mit: Francesco Maggi
Erscheinungsdatum: 03.08.2016
Gewicht: 0,919 kg
preigu-id: 106438158
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