Abstract
We study the microlocal analyticity and smoothness of solutions u of of the nonlinear PDE u t = f (x, t, u, u x ) under some assumptions on the repeated brackets of the linearized operator and its conjugate.
Résumé
Nous étudions l’analyticité microlocale et la régularité des solutions u de l’EDP non linéaire u t = f (x, t, u, u x ) sous certaines conditions portant sur les crochets itérés de l’opérateur linéarisé et de son conjugué.
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S. Berhanu’s work supported in part by NSF DMS 1001283.
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Adwan, Z., Berhanu, S. On microlocal analyticity and smoothness of solutions of first-order nonlinear PDEs. Math. Ann. 352, 239–258 (2012). https://doi.org/10.1007/s00208-011-0638-3
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DOI: https://doi.org/10.1007/s00208-011-0638-3