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"In this monograph, Cirant et al. prove comparison principles for nonlinear potential theories in Euclidian spaces in a straightforward manner from duality and monotonicity. They also show how to deduce comparison principles for nonlinear differential operators--a program seemingly different from the first. However, this monograph marries these two points of view, for a wide variety of equations, under something called the correspondence principle. Making this connection between potential theory and operator theory enables simplifications on the operator side and provides enrichment on the potential side. Harvey and Lawson have worked for 15 years to articulate a geometric approach to viscosity solutions for an important class of differential equations. Their approach is broader and more flexible than existing alternatives. With the collaboration of Cirant and Payne, this concise book establishes the keystone of the theory: the existence of comparison principles"--
About the author
Marco Cirant is associate professor of mathematical analysis at the Università di Padova.
F. Reese Harvey is professor emeritus of mathematics at Rice University and the author of
Spinors and Calibrations. H. Blaine Lawson is distinguished professor of mathematics at Stony Brook University, a member of the National Academy of Sciences, and the author of six books, including
Spin Geometry, with Marie-Louise Michelsohn (Princeton).
Kevin R. Payne is associate professor of mathematical analysis at the Università di Milano and a Fellow of the American Mathematical Society.
