Ebenfelt, Peter

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Ebenfelt, Peter
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Ebenfelt, Peter

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  • Publication
    The Goursat problem for a generalized Helmholtz operator in the plane
    (Springer, 2008-09)
    Ebenfelt, Peter 
    ;
    Render, Hermann 
    We consider the Goursat problem in the plane for partial differential operators whose principal part is the pth power of the standard Laplace operator. The data is posed on a union of 2p distinct lines through the origin. We show that the solvability of this Goursat problem depends on Diophantine properties of the geometry of lines on which the data is posed.
      481Scopus© Citations 6
  • Publication
    On the mixed Cauchy problem with data on singular conics
    (OUP, 2008-08)
    Ebenfelt, Peter 
    ;
    Render, Hermann 
    We consider a problem of mixed Cauchy type for certain holomorphic partial differential operators with the principal part Q2p(D) essentially being the (complex) Laplace operator to a power, Δp. We provide inital data on a singular conic divisor given by P = 0, where P is a homogeneous polynomial of degree 2p. We show that this problem is uniquely solvable if the polynomial P is elliptic, in a certain sense, with respect to the principal part Q2p(D).
      266Scopus© Citations 5