TY - JOUR
T1 - Approximate solutions of vector fields and an application to Denjoy–Carleman regularity of solutions of a nonlinear PDE
AU - Braun Rodrigues, Nicholas
AU - da Silva, Antonio Victor
N1 - Publisher Copyright:
© 2021 Wiley-VCH GmbH
PY - 2021/8
Y1 - 2021/8
N2 - In this paper we study microlocal regularity of a (Formula presented.) -solution u of the equation (Formula presented.) where (Formula presented.) is ultradifferentiable in the variables (Formula presented.) and holomorphic in the variables (Formula presented.). We proved that if (Formula presented.) is a regular Denjoy–Carleman class (including the quasianalytic case) then: (Formula presented.) where (Formula presented.) is the Denjoy–Carleman wave-front set of u and (Formula presented.) is the characteristic set of the linearized operator (Formula presented.) : (Formula presented.)
AB - In this paper we study microlocal regularity of a (Formula presented.) -solution u of the equation (Formula presented.) where (Formula presented.) is ultradifferentiable in the variables (Formula presented.) and holomorphic in the variables (Formula presented.). We proved that if (Formula presented.) is a regular Denjoy–Carleman class (including the quasianalytic case) then: (Formula presented.) where (Formula presented.) is the Denjoy–Carleman wave-front set of u and (Formula presented.) is the characteristic set of the linearized operator (Formula presented.) : (Formula presented.)
KW - Denjoy–Carleman approximate solutions
KW - Denjoy–Carleman wave-front set
KW - quasianalytic classes
UR - http://www.scopus.com/inward/record.url?scp=85111522012&partnerID=8YFLogxK
U2 - 10.1002/mana.201800516
DO - 10.1002/mana.201800516
M3 - Article
AN - SCOPUS:85111522012
SN - 0025-584X
VL - 294
SP - 1452
EP - 1471
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 8
ER -