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Boundary Value Problems for the Stokes System in Arbitrary Lipschitz Domains [Mīkstie vāki]

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  • Formāts: Paperback / softback, 241 pages, height x width: 229x152 mm, Illustrations
  • Izdošanas datums: 15-Jul-2010
  • Izdevniecība: Societe mathematique de France
  • ISBN-10: 2856293433
  • ISBN-13: 9782856293430
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Boundary Value Problems for the Stokes System in Arbitrary Lipschitz DomainsPalielināt
  • Formāts: Paperback / softback, 241 pages, height x width: 229x152 mm, Illustrations
  • Izdošanas datums: 15-Jul-2010
  • Izdevniecība: Societe mathematique de France
  • ISBN-10: 2856293433
  • ISBN-13: 9782856293430
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9782856293430.html
Keywords:
The goal of this work is to treat the main boundary value problems for the Stokes system, i.e., (i) the Dirichlet problem with Lp-data and nontangential maximal function estimates, (ii) the Neumann problem with Lp-data and nontangential maximal function estimates, (iii) the Regularity problem with Lp1-data and nontangential maximal function estimates, (iv) the transmission problem with Lp-data and nontangential maximal function estimates, (v) the Poisson problem with Dirichlet condition in Besov-Triebel-Lizorkin spaces, (vi) the Poisson problem with Neumann condition in Besov-Triebel-Lizorkin spaces, in Lipschitz domains of arbitrary topology in Rn, for each n [ greater than or equal to] 2. Our approach relies on boundary integral methods and yields constructive solutions to the aforementioned problems.
1 Introduction
1(16)
1.1 Description of main well-posedness results
1(10)
1.2 Consequences of the solvability of the inhomogeneous problem
11(6)
Acknowledgments
16(1)
2 Smoothness spaces and Lipschitz domains
17(24)
2.1 Graph Lipschitz domains
17(3)
2.2 Hardy spaces on graph Lipschitz surfaces
20(8)
2.3 Bounded Lipschitz domains
28(3)
2.4 Besov and Triebel-Lizorkin spaces in Lipschitz domains
31(4)
2.5 Smoothness spaces on Lipschitz boundaries
35(6)
3 Rellich identities for divergence form, second-order systems
41(8)
3.1 Green formulas
41(2)
3.2 A general Rellich identity for second order systems
43(6)
4 The Stokes system and hydrostatic potentials
49(28)
4.1 Bilinear forms and conormal derivatives
49(3)
4.2 Hydrostatic layer potential operators
52(10)
4.3 Traces of hydrostatic layer potentials in Hardy spaces
62(2)
4.4 Integral representation formulas
64(5)
4.5 Boundary integral operators and the transmission problem
69(8)
5 The LP transmission problem with p near 2
77(42)
5.1 Rellich identities and related estimates
77(9)
5.2 The case of a graph Lipschitz domain
86(6)
5.3 Inverting the double layer on LP for p near 2 on bounded Lipschitz domains
92(12)
5.4 Inverting the single layer on LP for p near 2 on bounded Lipschitz domains
104(3)
5.5 LP-boundary value problems on bounded Lipschitz domains for p near 2
107(12)
6 Local L2 estimates
119(10)
6.1 Pressure, Caccioppoli, and local boundary estimates
119(7)
6.2 Reverse Holder estimates
126(3)
7 The transmission problem in two and three dimensions
129(18)
7.1 Uniqueness
129(6)
7.2 Atomic estimates
135(8)
7.3 Interpolation arguments
143(4)
8 Higher dimensions
147(12)
8.1 Preliminary estimates
148(8)
8.2 The Dirichlet problem
156(3)
9 Boundary value problems in bounded Lipschitz domains
159(18)
9.1 Localization arguments
159(11)
9.2 Main well-posedness results with nontangential maximal function estimates
170(7)
10 The Poisson problem for the Stokes system
177(20)
10.1 Stokes-Besov and Stokes-Triebel-Lizorkin spaces
177(2)
10.2 Conormal derivatives on Stokes-Besov and Stokes-Triebel-Lizorkin scales
179(3)
10.3 The conormal derivative of the Stokes-Newtonian potentials
182(4)
10.4 The conormal on Besov and Triebel-Lizorkin spaces: the general case
186(1)
10.5 Layer potentials on Besov and Triebel-Lizorkin spaces
187(3)
10.6 The Poisson problem with Dirichlet and Neumann boundary conditions
190(7)
11 Appendix
197(38)
11.1 Smoothness spaces in the Euclidean setting
197(1)
11.2 Gehring's lemma
198(5)
11.3 Hole-filling lemma
203(1)
11.4 Korn's inequality
204(2)
11.5 Hardy's estimate
206(4)
11.6 Traces in Hardy spaces
210(2)
11.7 Spaces of null-solutions of elliptic operators
212(2)
11.8 Singular integral operators on Sobolev-Besov spaces
214(1)
11.9 Functional analysis on quasi-Banach spaces
215(9)
11.10 Surface to surface change of variables
224(2)
11.11 Truncating singular integrals
226(3)
11.12 Approximating Lipschitz domains
229(6)
Bibliography 235