Elliptic PDEs, Measures and Capacities
From the Poisson Equation to Nonlinear Thomas–Fermi Problems
Augusto C. Ponce
Université catholique de Louvain, Belgium
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| FrontmatterDownload pp. i–iv | |
| PrefaceDownload pp. v–vi | |
| ContentsDownload pp. vii–x | |
| 0 | IntroductionDownload pp. 1–6 |
| 1 | The Laplacianpp. 7–19 |
| 2 | Poisson equationpp. 21–37 |
| 3 | Integrable versus measure datapp. 39–48 |
| 4 | Variational approachpp. 49–75 |
| 5 | Linear regularity theorypp. 77–93 |
| 6 | Comparison toolspp. 95–110 |
| 7 | Balayagepp. 111–121 |
| 8 | Precise representativepp. 123–137 |
| 9 | Maximal inequalitiespp. 139–153 |
| 10 | Sobolev and Hausdorff capacitiespp. 155–169 |
| 11 | Removable singularitiespp. 171–179 |
| 12 | Obstacle problemspp. 181–204 |
| 13 | Families of solutionspp. 205–213 |
| 14 | Strong approximation of measurespp. 215–234 |
| 15 | Traces of Sobolev functionspp. 235–255 |
| 16 | Trace inequalitypp. 257–274 |
| 17 | Critical embeddingpp. 275–297 |
| 18 | Quasicontinuitypp. 299–310 |
| 19 | Nonlinear problems with diffuse measurespp. 311–319 |
| 20 | Extremal solutionspp. 321–336 |
| 21 | Absorption problemspp. 337–350 |
| 22 | The Schrödinger operatorpp. 351–363 |
| Appendicesp. 365 | |
| A | Sobolev capacitypp. 367–383 |
| B | Hausdorff measurepp. 385–393 |
| C | Solutions and hints to the exercisespp. 395–413 |
| Bibliographypp. 415–447 | |
| Indexpp. 449–453 |