PI: Kenig DMS-9500725 Kenig will continue his research on the development of various aspects of harmonic analysis and theory application to partial differential equations. The main emphasis will be on the study of boundary value problems under minimal smoothness conditions, boundary unique continuation and the "big-bang" property of control theory, regularity of two-phase free boundary problems, and the well-posedness of nonlinear equations and systems arising in wave propagation. The necessary harmonic analysis methods for the study of these problems will be investigated concurrently. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.
