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Régularité microlocale pour des problèmes aux limites non linéaires. (Microlocal regularity for nonlinear boundary value problems). (French) Zbl 0615.35092
Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1984, Conf. No. 1, 7 p. (1984).
The author studies the reflection of singularities of solutions of nonlinear partial differential equations in a region with noncharacteristic boundary. She defines the notion of tangential paraproduct of two functions by modifyng the theory of J. M. Bony [Ann. Sci. Ec. Norm. Super., IV. Sér. 14, 209-246 (1981; Zbl 0495.35024)] and she obtains the theorem of tangential paralinearisation. The author applies these results to the study of the boundary regularity problem and obtains a Nierenberg type result.
Reviewer: S.Tajima
MSC:
35S15 Boundary value problems for PDEs with pseudodifferential operators
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35G30 Boundary value problems for nonlinear higher-order PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
Citations:
Zbl 0495.35024
Full Text: Numdam EuDML