Nonlinear Potential Theory and Weighted Sobolev Spaces, Issue 1736 (Google eBook)

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Springer Science & Business Media, Jun 21, 2000 - Mathematics - 173 pages
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The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
  

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Contents

I
1
III
2
V
3
VI
6
VII
7
VIII
10
IX
12
XI
15
XXXVII
92
XXXVIII
97
XL
99
XLI
104
XLII
108
XLIII
110
XLIV
113
XLV
115

XII
16
XIII
17
XIV
19
XV
23
XVI
25
XVII
37
XVIII
40
XIX
41
XX
44
XXI
47
XXII
49
XXIII
53
XXIV
54
XXV
58
XXVI
59
XXVII
62
XXVIII
69
XXIX
70
XXXI
75
XXXII
77
XXXIV
80
XXXV
88
XLVI
117
XLVII
120
XLVIII
121
XLIX
122
L
124
LI
127
LII
131
LIII
134
LIV
141
LV
142
LVI
144
LVII
148
LIX
149
LX
151
LXII
155
LXIII
156
LXIV
157
LXV
160
LXVI
163
LXVII
171
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Common terms and phrases

Popular passages

Page 166 - inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series, Studia Math. 49 (1974), 107-124.
Page 164 - CARLESON, L., Selected Problems on Exceptional Sets, Van Nostrand, Princeton, NJ, 1967.
Page 168 - Weighted Sobolev spaces and pseudodifferential operators with smooth symbols, Trans. Amer. Math. Soc. 269 (1982), 91-109.
Page 170 - WIENER, N., The Dirichlet problem, J. Math, and Phys. 3 (1924), 127146.
Page 168 - imbedding theorems and the spectrum of a selfadjoint elliptic operator, Izv. Akad. Nauk SSSR, Ser. Mat. 37 (1973), 356-385
Page 169 - SOBOLEV, SL, On a boundary value problem for polyharmonic equations, Mat. Sb. (NS) 2
Page 164 - for an arbitrary open set fi, Trudy. Mat. Inst. Steklov., 131 (1974) 51-63

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