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Harmonic Analysis and Boundary Value Problems
Edited by: Luca Capogna and Loredana Lanzani, University of Arkansas, Fayetteville, AR
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Contemporary Mathematics
2001; 158 pp; softcover
Volume: 277
ISBN-10: 0-8218-2745-6
ISBN-13: 978-0-8218-2745-1
List Price: US$50
Member Price: US$40
Order Code: CONM/277
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This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on "Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View" held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations.

The following topics are featured: the solution of the Kato conjecture, the "two bricks" problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.

Readership

Graduate students and research mathematicians interested in partial differential equations and potential theory.

Table of Contents

  • J. D. Sykes and R. M. Brown -- The mixed boundary problem in \(L^p\) and Hardy spaces for Laplace's equation on a Lipschitz domain
  • D. Danielli, N. Garofalo, and D.-M. Nhieu -- Sub-elliptic Besov spaces and the characterization of traces on lower dimensional manifolds
  • S. Hofmann -- The solution of the Kato problem
  • M. B. Korey -- A decomposition of functions with vanishing mean oscillation
  • D. Mitrea and M. Mitrea -- General second order, strongly elliptic systems in low dimensional nonsmooth manifolds
  • E. Ferretti and M. V. Safonov -- Growth theorems and Harnack inequality for second order parabolic equations
  • Z. Shen -- Absolute continuity of generalized periodic Schrödinger operators
  • G. C. Verchota -- The use of Rellich identities on certain nongraph boundaries
  • J. Verdera -- \(L^2\) boundedness of the Cauchy integral and Menger curvature
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