This project will support research on several problems in the areas of nonlinear harmonic analysis and partial differential equations. Among the topics to be studied are the method of layer potentials for the heat equation in time-varying domains, Hardy spaces and boundary value problems for operators of Dirac type on Lipschitz domains, the characterization of the spaces of uniform holomorphy for partial sum operators for classical expansions, the calculation of the spectral radius of the trace of the double-layer potential for harmonic functions in certain domains, and applications of nonlinear harmonic analysis to problems in nonlinear partial differential equations. Nonlinear harmonic analysis emerged and developed in response to the challenges posed by difficult problems in classical analysis, particularly, but not exclusively, those arising from the study of partial differential equations. It is anticipated that applications of this work will lead to a better understanding of potential theory and the parabolic partial differential equations of heat flow.
