ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Sobolev Spaces in Mathematics I Sobolev Type Inequalities

:	Vladimir Maz'ya
:	Vladimir Maz'ya
:	Sobolev Spaces in Mathematics I Sobolev Type Inequalities
:	Springer-Verlag
:	9780387856483
:	1
:	CHF 207.90
:

:	Analysis
:	English

:	378
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

This volume mark's the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.

	Contributors	12
	Contents	21
	My Love Affair with the Sobolev Inequality	26
	1 The Trace Inequality	29
	2 A Mixed Norm Inequality	32
	3 A Morrey–Sobolev Inequality	34
	4 A Morrey–Besov Inequality	37
	5 Exponential Integrability	38
	6 Vanishing Exponential Integrability	43
	7 Concluding Remarks	45
	References	46
	Maximal Functions in Sobolev Spaces	49
	1 Introduction	49
	2 Maximal Function Defined on the Whole Space	51
	2.1 Boundedness in Sobolev spaces	51
	2.2 A capacitary weak type estimate	56
	3 Maximal Function Defined on a Subdomain	57
	3.1 Boundedness in Sobolev spaces	57
	3.2 Sobolev boundary values	62
	4 Pointwise Inequalities	65
	4.1 Lusin type approximation of Sobolev functions	69
	5 Hardy Inequality	73
	6 Maximal Functions on Metric Measure Spaces	78
	6.1 Sobolev spaces on metric measure spaces	79
	6.2 Maximal function defined on the whole space	81
	6.3 Maximal function defined on a subdomain	86
	6.4 Pointwise estimates and Lusin type approximation	88
	References	89
	Hardy Type Inequalities via Riccati and Sturm– Liouville Equations	92
	1 Introduction	92
	2 Riccati Equations	94
	3 Transition to Sturm–Liouville Equations	98
	4 Hardy Type Inequalities with Weights	100
	5 Poincar´e Type Inequalities	106
	References	108
	Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles	110
	1 Introduction	110
	2 Symmetrization Inequalities	112
	2.1 Rearrangements of functions and function spaces	112
	2.2 The Hardy-Littlewood inequality	115
	2.3 The Polya-Szegö inequality	119
	3 Sobolev Inequalities	124
	3.1 Functions of Bounded Variation	124
	3.2 The case 1	124
	3.2 The case 1	124
	126	124
	3.3 The case p	124
	129	124
	4 Hardy Inequalities	131
	4.1 The case 1	131
	4.1 The case 1	131
	131	131
	4.2 The case p = n	134
	References	136
	Inequalities of Hardy–Sobolev Type in Carnot– Caratheodory Spaces	140
	1 Introduction	140
	2 Preliminaries	144
	3 Pointwise Hardy Inequalities	150
	4 Hardy Inequalities on Bounded Domains	162
	5 Hardy Inequalities with Sharp Constants	168
	References	172
	Sobolev Embeddings and Hardy Operators	175
	1 Introduction	175
	2 Hardy Operators on Trees	176
	3 The Poincare Inequality, a(E) and Hardy Type Operators	180
	4 Generalized Ridged Domains	184
	5 Approximation and Other s-Numbers of Hardy Type Operators	192
	6 Approximation Numbers of Embeddings on Generalized Ridged Domains	203
	References	204
	Sobolev Mappings between Manifolds and Metric Spaces	206
	1 Introduction	206
	2 Sobolev Mappings between Manifolds	208
	3 Sobolev Mappings into Metric Spaces	218
	3.1 Density	223
	4 Sobolev Spaces on Metric Measure Spaces	226
	4.