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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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Full text of review: PDF   This review is available free of charge.
Book Information:

Author: 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 pp., ISBN 0-8218-0309-3, $30.00$

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  • Ioannis Athanasopoulos and Luis A. Caffarelli, A theorem of real analysis and its application to free boundary problems, Comm. Pure Appl. Math. 38 (1985), no. 5, 499–502. MR 803243, DOI 10.1002/cpa.3160380503
  • N. E. Aguilera, L. A. Caffarelli, and J. Spruck, An optimization problem in heat conduction, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987), no. 3, 355–387 (1988). MR 951225
  • Russell M. Brown, The method of layer potentials for the heat equation in Lipschitz cylinders, Amer. J. Math. 111 (1989), no. 2, 339–379. MR 987761, DOI 10.2307/2374513
  • Sergio Campanato, A bound for the solutions of a basic elliptic system with nonlinearity $q\geq 2$, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 80 (1986), no. 3, 81–88 (1987) (English, with Italian summary). MR 976693
  • Luis A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. II. Flat free boundaries are Lipschitz, Comm. Pure Appl. Math. 42 (1989), no. 1, 55–78. MR 973745, DOI 10.1002/cpa.3160420105
  • A.-P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 4, 1324–1327. MR 466568, DOI 10.1073/pnas.74.4.1324
  • R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250
  • R. R. Coifman, D. G. Deng, and Y. Meyer, Domaine de la racine carrée de certains opérateurs différentiels accrétifs, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 2, x, 123–134 (French, with English summary). MR 699490
  • Luis A. Caffarelli, Eugene B. Fabes, and Carlos E. Kenig, Completely singular elliptic-harmonic measures, Indiana Univ. Math. J. 30 (1981), no. 6, 917–924. MR 632860, DOI 10.1512/iumj.1981.30.30067
  • L. Caffarelli, E. Fabes, S. Mortola, and S. Salsa, Boundary behavior of nonnegative solutions of elliptic operators in divergence form, Indiana Univ. Math. J. 30 (1981), no. 4, 621–640. MR 620271, DOI 10.1512/iumj.1981.30.30049
  • R. R. Coifman, A. McIntosh, and Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), no. 2, 361–387 (French). MR 672839, DOI 10.2307/2007065
  • A.-P. Calderón and A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171–225. MR 136849, DOI 10.4064/sm-20-2-181-225
  • Björn E. J. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), no. 3, 275–288. MR 466593, DOI 10.1007/BF00280445
  • Björn E. J. Dahlberg, On the absolute continuity of elliptic measures, Amer. J. Math. 108 (1986), no. 5, 1119–1138. MR 859772, DOI 10.2307/2374598
  • Ennio De Giorgi, Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3) 3 (1957), 25–43 (Italian). MR 0093649
  • Björn E. J. Dahlberg and Carlos E. Kenig, Hardy spaces and the Neumann problem in $L^p$ for Laplace’s equation in Lipschitz domains, Ann. of Math. (2) 125 (1987), no. 3, 437–465. MR 890159, DOI 10.2307/1971407
  • Eugene Fabes, The initial value problem for parabolic equations with data in $L^{p}(R^{n})$, Studia Math. 44 (1972), 389–409. MR 328356, DOI 10.4064/sm-44-4-389-409
  • Eugene B. Fabes, David S. Jerison, and Carlos E. Kenig, Multilinear Littlewood-Paley estimates with applications to partial differential equations, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), no. 18, 5746–5750. MR 674919, DOI 10.1073/pnas.79.18.5746
  • E. B. Fabes, M. Jodeit Jr., and N. M. Rivière, Potential techniques for boundary value problems on $C^{1}$-domains, Acta Math. 141 (1978), no. 3-4, 165–186. MR 501367, DOI 10.1007/BF02545747
  • R. Fefferman, A criterion for the absolute continuity of the harmonic measure associated with an elliptic operator, J. Amer. Math. Soc. 2 (1989), no. 1, 127–135. MR 955604, DOI 10.1090/S0894-0347-1989-0955604-8
  • R. A. Fefferman, C. E. Kenig, and J. Pipher, The theory of weights and the Dirichlet problem for elliptic equations, Ann. of Math. (2) 134 (1991), no. 1, 65–124. MR 1114608, DOI 10.2307/2944333
  • E. Fabes, S. Sroka, and K.-O. Widman, Littlewood-Paley a priori estimates for parabolic equations with sub-Dini continuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 6 (1979), no. 2, 305–334. MR 541451
  • Richard A. Hunt and Richard L. Wheeden, On the boundary values of harmonic functions, Trans. Amer. Math. Soc. 132 (1968), 307–322. MR 226044, DOI 10.1090/S0002-9947-1968-0226044-7
  • David S. Jerison and Carlos E. Kenig, The Dirichlet problem in nonsmooth domains, Ann. of Math. (2) 113 (1981), no. 2, 367–382. MR 607897, DOI 10.2307/2006988
  • F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415–426. MR 131498, DOI 10.1002/cpa.3160140317
  • Carlos E. Kenig and Jill Pipher, The Neumann problem for elliptic equations with nonsmooth coefficients, Invent. Math. 113 (1993), no. 3, 447–509. MR 1231834, DOI 10.1007/BF01244315
  • [KP2]
    ------, The Neumann problem for elliptic equations with non-smooth coefficients, Part 2, Duke J. Math. (to appear).
    N. Lim, The Dirichlet problem for elliptic equations with data in $L^p$, J. Funct. Anal. (to appear).
  • J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931–954. MR 100158, DOI 10.2307/2372841
  • Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6
  • Jürgen Moser, On Harnack’s theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577–591. MR 159138, DOI 10.1002/cpa.3160140329
  • J. Pipher and G. Verchota, A maximum principle for biharmonic functions in Lipschitz and $C^1$ domains, Comment. Math. Helv. 68 (1993), no. 3, 385–414. MR 1236761, DOI 10.1007/BF02565827
  • [PV2]
    ------, Maximum principles for the polyharmonic equation on Lipschitz domains, J. Potential Anal. (to appear).
  • Gregory Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains, J. Funct. Anal. 59 (1984), no. 3, 572–611. MR 769382, DOI 10.1016/0022-1236(84)90066-1
  • Mary Weiss and Antoni Zygmund, A note on smooth functions, Nederl. Akad. Wetensch. Proc. Ser. A 62 = Indag. Math. 21 (1959), 52–58. MR 0107122
  • [Z]
    S. Zaremba, Sur le principe de Dirichlet, Acta Math. 34 (1911), 293--316.

    Review Information:

    Reviewer: Jill C. Pipher
    Affiliation: Brown University
    Journal: Bull. Amer. Math. Soc. 33 (1996), 229-236
    Review copyright: © Copyright 1996 American Mathematical Society