Elliptic PDEs, Measures and Capacities

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From the Poisson Equation to Nonlinear Thomas–Fermi Problems

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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