AMERICAN MATHEMATICAL SOCIETY 107
Harmonic Analysis and Partial Differential Equations
Proceedings of a Conference held April 4-5, 1988 http://dx.doi.org/10.1090/conm/107 Titles in This Series
Volume 1 Markov random fields and their 19 Proceedings of the Northwestern applications, Ross Kindermann and homotopy theory conference, Haynes J. Laurie Snell R. Miller and Stewart B. Priddy, Editors 2 Proceedings of the conference on 20 Low dimensional topology, Samuel J. integration, topology, and geometry in Lomonaco, Jr., Editor linear spaces, William H. Graves, Editor 21 Topological methods in nonlinear 3 The closed graph and P-closed functional analysis, S. P. Singh, graph properties in general topology, S. Thomaier, and B. Watson, Editors T. R. Hamlett and L. L. Herrington 22 Factorizations of b" ± 1, b = 2, 4 Problems of elastic stability and 3, 5, 6, 7, 10, 11, 12 up to high vibrations, Vadim Komkov, Editor powers, John Brillhart, D. H. Lehmer, 5 Rational constructions of modules J. L. Selfridge, Bryant Tuckerman, and for simple Lie algebras, George B. S. S. Wagstaff, Jr. Seligman 23 Chapter 9 of Ramanujan's second 6 Umbral calculus and Hopf algebras, notebook-Infinite series identities, Robert Morris, Editor transformations, and evaluations, Bruce C. Berndt and Padmini T. Joshi 7 Complex contour integral representation of cardinal spline 24 Central extensions, Galois groups, and functions, Walter Schempp ideal class groups of number fields, A. Frohlich 8 Ordered fields and real algebraic geometry, D. W. Dubois and T. Recio, 25 Value distribution theory and its Editors applications, Chung-Chun Yang, Editor 9 Papers in algebra, analysis and 26 Conference in modern analysis statistics, R. Lidl, Editor and probability, Richard Beals, 10 Operator algebras and K-theory, Anatole Beck, Alexandra Bellow, and Ronald G. Douglas and Claude Arshag Hajian, Editors Schochet, Editors 27 Microlocal analysis, M. Salah Baouendi, 11 Plane ellipticity and related problems, Richard Beals, and Linda Preiss Robert P. Gilbert, Editor Rothschild, Editors 12 Symposium on algebraic topology in 28 Fluids and plasmas: geometry and honor of Jose Adem, Samuel Gitler, dynamics, Jerrold E. Marsden, Editor Editor 29 Automated theorem proving, W. W. 13 Algebraists' homage: Papers in Bledsoe and Donald Loveland, Editors ring theory and related topics, 30 Mathematical applications of category S. A. Amitsur, D. J. Saltman, and theory, J. W. Gray, Editor G. B. Seligman, Editors 31 Axiomatic set theory, James E. 14 Lectures on Nielsen fixed point theory, Baumgartner, Donald A. Martin, and Boju Jiang Saharon Shelah, Editors 15 Advanced analytic number theory. 32 Proceedings of the conference on Part 1: Ramification theoretic methods, Banach algebras and several complex Carlos J. Moreno variables, F. Greenleaf and D. Gulick, 16 Complex representations of GL(2, K) for Editors finite fields K, llya Piatetski-Shapiro 33 Contributions to group theory, 17 Nonlinear partial differential equations, Kenneth I. Appel, John G. Ratcliffe, and Joel A. Smeller, Editor Paul E. Schupp, Editors 18 Fixed points and nonexpansive 34 Combinatoric& and algebra, Curtis mappings, Robert C. Sine, Editor Greene, Editor Titles in This Series
Volume 35 Four-manifold theory, Cameron Gordon 53 The Selberg trace formula and related and Robion Kirby, Editors topics, Dennis A. Hejhal, Peter Sarnak, 36 Group actions on manifolds, Reinhard and Audrey Anne Terras, Editors Schultz, Editor 54 Differential analysis and infinite 37 Conference on algebraic topology in dimensional spaces, Kondagunta honor of Peter Hilton, Renzo Piccinini Sundaresan and Srinivasa Swaminathan, and Denis Sjerve, Editors Editors 38 Topics in complex analysis, Dorothy 55 Applications of algebraic K-theory to Browne Shaffer, Editor algebraic geometry and number theory, 39 ErreH Bishop: Reflections on him and Spencer J. Bloch, R. Keith Dennis, Eric his research, Murray Rosenblatt, Editor M. Friedlander, and Michael R. Stein, Editors 40 Integral bases for affine Lie algebras and their universal enveloping algebras, 56 Multiparameter bifurcation theory, David Mitzman Martin Golubitsky and 41 Particle systems, random media and John Guckenheimer, Editors large deviations, Richard Durrett, Editor 57 Combinatorics and ordered sets, 42 Classical real analysis, Daniel Ivan Rival, Editor Waterman, Editor 58.1 The Lefschetz centennial conference. 43 Group actions on rings, Susan Proceedings on algebraic geometry, Montgomery, Editor D. Sundararaman, Editor 44 Combinatorial methods in topology and 58.11 The Lefschetz centennial conference. algebraic geometry, John R. Harper Proceedings on algebraic topology, and Richard Mandelbaum, Editors S. Gitler, Editor 45 Finite groups-coming of age, John 58.111 The Lefschetz centennial conference. McKay, Editor Proceedings on differential equations, 46 Structure of the standard modules A. Verjovsky, Editor for the affine Lie algebra Ap>, 59 Function estimates, J. S. Marron, Editor James Lepowsky and Mirko Prime 60 Nonstrictly hyperbolic conservation 47 Linear algebra and its role in laws, Barbara Lee Keyfitz and systems theory, Richard A. Brualdi, Herbert C. Kranzer, Editors David H. Carlson, Biswa Nath Datta, Charles R. Johnson, and Robert J. 61 Residues and traces of differential Plemmons, Editors forms via Hochschild homology, 48 Analytic functions of one complex Joseph Lipman variable, Chung-chun Yang and 62 Operator algebras and mathematical Chi-tai Chuang, Editors physics, Palle E. T. Jorgensen and 49 Complex differential geometry and PaulS. Muhly, Editors nonlinear differential equations, 63 Integral geometry, Robert L. Bryant, Yum-Tong Siu, Editor Victor Guillemin, Sigurdur Helgason, and 50 Random matrices and their R. 0. Wells, Jr., Editors applications, Joel E. Cohen, 64 The legacy of Sonya Kovalevskaya, Harry Kesten, and Charles M. Newman, Linda Keen, Editor Editors 65 Logic and combinatorics, Stephen G. 51 Nonlinear problems in geometry, Simpson, Editor Dennis M. DeTurck, Editor Free group rings, Narian Gupta 52 Geometry of normed linear spaces, 66 R. G. Bartle, N. T. Peck, A. L. Peressini, 67 Current trends in arithmetical algebraic and J. J. Uhl, Editors geometry, Kenneth A. Ribet, Editor Titles in This Series
Volume 68 Differential geometry: The interface 86 Representation theory and number between pure and applied mathematics, theory in connection with the local Mladen Luksic, Clyde Martin, and Langlands conjecture, J. Ritter, Editor William Shadwick, Editors 87 Abelian group theory, Laszlo Fuchs, 69 Methods and applications of Rudiger Gobel, and Phillip Schultz, mathematical logic, Walter A. Carnielli Editors and Luiz Paulo de Alcantara, Editors 88 Invariant theory, R. Fossum, 70 Index theory of elliptic operators, W. Haboush, M. Hochster, and foliations, and operator algebras, V. Lakshmibai, Editors Jerome Kaminker, Kenneth C. Millett, 89 Graphs and algorithms, R. Bruce and Claude Schochet, Editors Richter, Editor 71 Mathematics and general relativity, 90 Singularities, Richard Randell, Editor James A. Isenberg, Editor 91 Commutative harmonic analysis, 72 Fixed point theory and its applications, David Colella, Editor R. F. Brown, Editor 92 Categories in. computer science and 73 Geometry of random motion, Rick logic, John W. Gray and Andre Scedrov, Durrett and Mark A. Pinsky, Editors Editors 93 Representation theory, group rings, and 74 Geometry of group representations, coding theory, M. Isaacs, A. Lichtman, William M. Goldman and Andy R. Magid, D. Passman, S. Sehgal, N.J. A. Sloane, Editors and H. Zassenhaus, Editors 75 The finite calculus associated with 94 Measure and measurable dynamics, Bessel functions, Frank M. Cholewinski R. Daniel Mauldin, R. M. Shortt, and 76 The structure of finite algebras, Cesar E. Silva, Editors David C. Hobby and Ralph Mckenzie 95 Infinite algebraic extensions of finite 77 Number theory and its applications in fields, Joel V. Brawley and George E. China, Wang Yuan, Yang Chung-chun, Schnibben and Pan Chengbiao, Editors 96 Algebraic topology, Mark Mahowald 78 Braids, Joan S. Birman and Anatoly and Stewart Priddy, Editors Libgober, Editors 97 Dynamics and control of multibody 79 Regular differential forms, Ernst Kunz systems, J. E. Marsden, P. S. and Rolf Waldi Krishnaprasad, and J. C. Simo, Editors 80 Statistical inference from stochastic 98 Every planar map is four colorable, processes, N. U. Prabhu, Editor Kenneth Appel and Wolfgang Haken 99 The connection between infinite 81 Hamiltonian dynamical systems, dimensional and finite dimensional Kenneth R. Meyer and Donald G. Saari, dynamical systems, Basil Nicolaenko, Editors Ciprian Foias, and Roger Temam, 82 Classical groups and related topics, Editors Alexander J. Hahn, Donald G. James, 100 Current progress in hyperbolic systems: and Zhe-xian Wan, Editors Riemann problems and computations, 83 Algebraic K-theory and algebraic W. Brent Lindquist, Editor number theory, Michael R. Stein and 101 Recent developments in geometry, R. Keith Dennis, Editors S.-Y. Cheng, H. Choi, and Robert E. 84 Partition problems in topology, Greene, Editors Stevo Todorcevic 102 Primes associated to an ideal, 85 Banach space theory, Bor-Luh Lin, Stephen McAdam Editor 103 Coloring theories, Steve Fisk Titles in This Series
Volume 104 Accessible categories: The foundations of categorical model theory, Michael Makkai and Robert Pare 105 Geometric and topological invariants of elliptic operators, Jerome Kaminker, Editor 106 Logic and computation, Wilfried Sieg, Editor 107 Harmonic Analysis and Partial Differential Equations, Mario Milman and Tomas Schonbek, Editors Harmonic Analysis and Partial Differential Equations ONTEMPORARY ATHEMATICS
107
Harmonic Analysis and Partial Differential Equations
Proceedings of a Conference held April 4-5, 1988
Mario Milman and Tomas Schonbek, Editors
AMERICAN MATHEMATICAL SOCIETY • PROVIDENCE, RHODE ISLAND EDITORIAL BOARD
Richard W. Beals, managing editor Sylvain E. Cappel! Jan Mycielski Jonathan Goodman Linda Preiss Rothschild Craig Huneke Michael E. Taylor
The Conference on Harmonic Analysis and Partial Differential Equations was held at the Florida Atlantic University, Boca Raton, Florida on April 4-5, 1988.
1980 Mathematics Subject Classification {1985 Revision). Primary 35-06, 42-06.
Library of Congress Cataloging-in-Publication Data Harmonic Analysis and Partial Differential Equations {1988: Florida Atlantic University) Harmonic analysis and partial differential equations: proceedings of the conference held April 4-5, 1988/Mario Milman and Tomas Schonbek, editors. p. cm.-(Contemporary mathematics, ISSN 0271-4132; v. 107) "The Conference on Harmonic Analysis and Partial Differential Equations was held at the Florida Atlantic University, Boca Raton, Florida on April 4-5, 1988""-T.p. verso. Includes bibliographical references. ISBN 0-8218-5113-6 (alk. paper) 1. Harmonic analysis-Congresses. 2. Differential equations, Partial-Congresses. I. Milman, Mario. II. Schonbek, Tomas, 1944-. Ill. Title. IV. Series: Contemporary mathematics (American Mathematical Society); v. 107. QA403.H236 1988 90-34635 5151 .2433-dc20 CIP
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Preface Xl Gradient Estimates at the Boundary for Solutions to Nondivergence Elliptic Equations B. BARCELO, L. ESCAURIAZA, and E. F ABES Interior Regularity of Solutions to Monge Ampere Equations L. A. CAFFARELLI 13 The Helson-Szego Theorem in U of the Bidimensional Torus M. COTLAR and C. SADOSKY 19 Galerkin Methods for the Boundary Integral Equations of Elliptic Equations in Nonsmooth Domains B. E. J. DAHLBERG and G. VERCHOTA 39 Some Applications of Hardy Spaces and BMO in Harmonic Analysis and Partial Differential Equations R. FEFFERMAN 61 The Positive Cone in Triebel-Lizorkin Spaces and the Relation Among Potential and Maximal Operators B. JAWERTH, C. PEREZ, and G. WELLAND 71 Changes of Variable and Ap Weights R. JOHNSON 93 Progress on Two Problems Posed by Riviere C. E. KENIG 101 Fredholm Theory for Periodic Solutions of Some Semilinear P.D.E.s with Homogeneous Nonlinearities A. C. LAZER and P. J. MCKENNA 109 Stability of Solitary Waves W. A. STRAUSS 123
IX Preface
In this volume we have collected, in final form, papers presented at the conference on Harmonic Analysis and Partial Differential Equations held April 4-5, 1988 at Florida Atlantic University. We thank the participants for their contributions which reflect the quality and the substance of the conference. We are also grateful to Florida At- lantic University for the financial support that made the program possible. A number of people contributed their time and energy helping to make the conference a success, in particular we thank Beth Broer, Jack Freeman, and Yanda Milman. Mario Milman Tomas Schonbek Boca Raton, Florida
XI .:·.-.
ISBN 978-0-8218-5113-5
9 780821 851135 CONM/107