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Book Review
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Book Information
Author(s):
Carlos E. Kenig
Title:
Harmonic analysis techniques for second order elliptic boundary value problems
Additional book information:
CBMS Regional Conf. Series in Math., no. 83, Amer. Math. Soc.,
Providence, RI,
1994,
xii + 146,
$30.00,
ISBN 0-8218-0309-3
References:
- [AC]
- I. Athanasopoulos and L. Caffarelli, A theorem of real analysis and its application to a free boundary problem, Comm. Pure Appl. Math. 38 (1985), 499--502. MR 86j:49062
- [AgCS]
- N. Aguilera, L. Caffarelli and J. Spruck, An optimization problem in heat conduction, Ann. Scuola Norm. Sup. Pisa 14 (1987), 355--387. MR 89h:49016
- [B]
- R. Brown, The method of layer potentials for the heat equation in Lipschitz cylinders, Amer. J. Math. 111 (1989), 339--379. MR 90d:35118
- [C1]
- L. Caffarelli, A Harnack inequality approach to the regularity of free boundaries, Part 1: Lipschitz free boundaries are
, Revista Mat. Ib. 3 (1987), 139--162. MR 90d:35036 - [C2]
- ------, A Harnack inequality approach to the regularity of free boundaries, Comm. Pure Appl. Math. 42 (1989), 55--78. MR 90b:35246
- [Ca]
- A. P. Calderón, Cauchy integrals in Lipschitz curves and related operators, Proc. Nat. Acad. Sci. USA 74 (1977), 1324--1327. MR 57:6445
- [CF]
- R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241--250. MR 50:10670
- [CDM]
- R. Coifman, D. Deng, and Y. Meyer, Domaine de la racine carrée de certains operateurs differentiels accrétifs, Ann. Inst. Fourier 33 (1983), 123--134. MR 84h:35040
- [CFK]
- L. Caffarelli, E. Fabes, and C. Kenig, Completely singular elliptic-harmonic measures, Indiana U. Math. J. 30 (1981), 189--213. MR 83a:35033
- [CFMS]
- L. Cafarelli, E. Fabes, S. Mortola, and S. Salsa, Boundary behavior of non-negative solutions of elliptic operators in divergence form, Ind. U. Math. J. 30 (1981), 621--640. MR 83c:35040
- [CMcM]
- R. Coifman, A. McIntosh, and Y. Meyer, L'intégrale de Cauchy définit un opérateur borné sur
pour les courbes lipschitziennes, Ann. of Math. 116 (1982), 361--387. MR 84m:42027 - [CZ]
- A. Calderón and A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171--225. MR 25:310
- [D1]
- B. Dahlberg, On estimates for harmonic measure, Arch. Rat. Mech. Anal. 56 (1977), 272--288. MR 57:6470
- [D2]
- ------, On the absolute continuity of elliptic measures, Amer. J. Math. 108 (1986), 1119--1138. MR 88i:35061
- [De]
- E. De. Giorgi, Sulla differenziabilita e analiticita delle estremali degli integrali multipli regolari, Mem. Acad. Sci. Torino 3 (1957), 25--43. MR 20:172
- [DK]
- B. E. J. Dahlberg and C. Kenig, Hardy spaces and the
-Neumann problem for Laplace's equation in a Lipschitz domain, Ann. of Math. 125 (1987), 437--465. MR 88d:35044 - [Fa]
- E. Fabes, The initial value problem for parabolic equations with data in
, Studia Math. 44 (1972), 89--109. MR 48:6698 - [FJK]
- E. Fabes, D. Jerison, and C. Kenig, Multilinear Littlewood-Paley estimates with applications to partial differential equations, Proc. Nat. Acad. Sci. USA 79 (1982), 5746--5750. MR 83k:47035
- [FJR]
- E. Fabes, M. Jodeit, and N. Riviere, Potential techniques for boundary value problems on
domains, Acta Math. 141 (1978), 165--186. MR 80b:31006 - [Fe]
- R. Fefferman, A criterion for the absolute continuity of the harmonic measure associated with an elliptic operator, J. Amer. Math. Soc. 2 (1989), 127--135. MR 90b:35068
- [FeKP]
- R. A. Fefferman, C. E. Kenig, and J. Pipher, The theory of weights and the Dirichlet problem for elliptic equations, Ann. of Math. 134 (1991), 65--124. MR 93h:31010
- [FSW]
- E. Fabes, S. Sroka, and K. Widman, Littlewood-Paley estimates for parabolic equations with sub-Dini continuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 6 (1979), 305--334. MR 80h:35072
- [HW]
- R. Hunt and R. Wheeden, On the boundary values of harmonic functions, Trans. Amer. Math. Soc. 132 (1968), 307--322. MR 37:1634
- [JK]
- D. Jerison and C. Kenig, The Dirichlet problem on non-smooth domains, Ann. of Math. 113 (1981), 367--382. MR 84j:35076
- [JN]
- F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415--426. MR 24:A1348
- [KP1]
- C. Kenig and J. Pipher, The Neumann problem for elliptic equations with non-smooth coefficients, Invent. Math. 113 (1993), 447--509. MR 95b:35046
- [KP2]
- ------, The Neumann problem for elliptic equations with non-smooth coefficients, Part 2, Duke J. Math. (to appear).
- [L]
- N. Lim, The Dirichlet problem for elliptic equations with data in
, J. Funct. Anal. (to appear). - [Na]
- J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931--954. MR 20:6592
- [M]
- B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal functions, Trans. Amer. Math. Soc. 165 (1972), 207--226. MR 45:2461
- [Mo]
- J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577--591. MR 28:2356
- [PV1]
- J. Pipher and G. Verchota, A maximum principle for biharmonic functions in Lipschitz and
domains, Comm. Math. Helv. 68 (1993), 385--414. MR 94j:35030 - [PV2]
- ------, Maximum principles for the polyharmonic equation on Lipschitz domains, J. Potential Anal. (to appear).
- [V]
- G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation, J. Funct. Anal. 59 (1984), 572--611. MR 86e:35038
- [WZ]
- M. Weiss and A. Zygmund, A note on smooth functions, Indag. Math. 62 (1959), 52--58. MR 21:5849
- [Z]
- S. Zaremba, Sur le principe de Dirichlet, Acta Math. 34 (1911), 293--316.
Additional Information:
Reviewer(s):
Jill
C.
Pipher
Affiliation:
Brown University
Email:
jpipher@math.brown.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
33
(1996),
229-236.
DOI:
10.1090/S0273-0979-96-00637-4
PII:
S 0273-0979(96)00637-4
Copyright of article:
Copyright
1996,
American Mathematical Society
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