By Michael Eugene Taylor
This ebook develops 3 similar instruments which are worthy within the research of partial differential equations (PDEs), coming up from the classical examine of singular quintessential operators: pseudodifferential operators, paradifferential operators, and layer potentials. A topic operating in the course of the paintings is the therapy of PDE in the presence of really little regularity. the 1st bankruptcy stories sessions of pseudodifferential operators whose symbols have a restricted measure of regularity; the second one bankruptcy indicates how paradifferential operators yield sharp estimates at the motion of assorted nonlinear operators on functionality areas. The 3rd bankruptcy applies this fabric to an collection of effects in PDE, together with regularity effects for elliptic PDE with tough coefficients, planar fluid flows on tough domain names, estimates on Riemannian manifolds given vulnerable bounds on Ricci tensor, div-curl estimates, and effects on propagation of singularities for wave equations with tough coefficients. The final bankruptcy stories the approach to layer potentials on Lipschitz domain names, concentrating on purposes to boundary difficulties for elliptic PDE with variable coefficients. Michael Taylor is the writer of numerous famous books on themes in PDEs and pseudodifferential operators. His "Noncommutative Harmonic Analysis", quantity 22 within the Mathematical Surveys and Monographs sequence released via the AMS, is an efficient advent to using Lie teams in linear research and PDEs. the current ebook, instruments for PDE, is appropriate as a textual content for complicated graduate scholars getting ready to pay attention in PDE and/or harmonic research.