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Calcul paradifférentiel précisé et applications à des équations aux dérivées partielles non semilinéaires. (Precise paradifferential calculus and applications to non-semilinear partial differential equations). (French) Zbl 0676.35009
Regularity results for solutions of the equation \(f(x,u,\partial^{\beta}u)_{| \beta | \leq m}=0,\) \(f\in C^{\infty}\), are proved either in the first order case or in the case of dimension 2. To do this the author studies in a first stage a so- called precised paradifferential calculus.
Reviewer: G.Moroşanu

MSC:
35B65 Smoothness and regularity of solutions to PDEs
35G20 Nonlinear higher-order PDEs
35F20 Nonlinear first-order PDEs
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