This publication develops 3 similar instruments which are necessary within the research of partial differential equations (PDEs), bobbing up from the classical learn of singular indispensable operators: pseudodifferential operators, paradifferential operators, and layer potentials. A topic operating in the course of the paintings is the therapy of PDE within the presence of particularly 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 ends up 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 reports the strategy of layer potentials on Lipschitz domain names, targeting purposes to boundary difficulties for elliptic PDE with variable coefficients.
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