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On the mixed Cauchy problem with data on singular conics
Author(s) -
Ebenfelt Peter,
Render Hermann
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn028
Subject(s) - mathematics , conic section , holomorphic function , polynomial , mathematical analysis , operator (biology) , pure mathematics , differential operator , cauchy's integral formula , cauchy principal value , homogeneous polynomial , cauchy problem , cauchy distribution , laplace operator , principal part , degree (music) , matrix polynomial , initial value problem , boundary value problem , cauchy boundary condition , neumann boundary condition , geometry , biochemistry , chemistry , physics , repressor , transcription factor , acoustics , gene
We consider a problem of mixed Cauchy type for certain holomorphic partial differential operators with the principal part Q 2 p ( D ) essentially being the (complex) Laplace operator to a power, Δ p . We provide inital data on a singular conic divisor given by P = 0, where P is a homogeneous polynomial of degree 2 p . We show that this problem is uniquely solvable if the polynomial P is elliptic, in a certain sense, with respect to the principal part Q 2 p ( D ).