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382 results in 35Jxx

Page 20 of 20

  • On a method for constructing Bergman kernels

  • Part of
  • A. Azzam, E. Kreyszig
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 29 / Issue 4 / June 1980
    Published online by Cambridge University Press:
    09 April 2009, pp. 454-461
    Print publication:
    June 1980
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  • We establish a method of constructing kernels of Bergman operators for second-order linear partial differential equations in two independent variables, and use the method for obtaining a new class of Bergman kernels, which we call modified class E kernels since they include certain class E kernals. They also include other kernels which are suitable for global representations of solutions (whereas Bergman operators generally yield only local representations).

  • Second order elliptic boundary value problems in spaces with homogeneous norms

  • Part of
  • A. J. Pryde
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 29 / Issue 1 / February 1980
    Published online by Cambridge University Press:
    09 April 2009, pp. 1-13
    Print publication:
    February 1980
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  • We consider the interior and Dirichiet problems and problems with first order boundary conditions, for a second order homogeneous elliptic partial differential operator with constant coefficients. Under natural conditions on the operators, these problems give rise to isomorphisms between the appropriate spaces with homogeneous norms. From there we obtain a priori estimates and regularity results for boundary value problems in Sobolev spaces.

Page 20 of 20