Contemporary Mathematics 2001; 158 pp; softcover Volume: 277 ISBN10: 0821827456 ISBN13: 9780821827451 List Price: US$53 Member Price: US$42.40 Order Code: CONM/277
 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 nonsmooth curves, the Neumann problem for subLaplacians, 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  Subelliptic 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
