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Annali di Matematica Pura ed Applicata

, Volume 110, Issue 1, pp 223–245 | Cite as

Boundary value problems for nonuniformly elliptic equations with measurable coefficients

  • C. V. Coffman
  • M. M. Marcus
  • V. J. Mizel
Article

Summary

Let A be a symmetric N × N real-matrix-valued function on a connected region in Rn, with A positive definite a.e. and A, A−1 locally integrable. Let b and c be locally integrable, non-negative, real-valued functions on Ω, with c positive a.e. Put a(u, v) = =\(\mathop \smallint \limits_\Omega \)((A∇u, ∇v) + buv) dx. We consider in X the weak boundary value problem a(u, v) = =\(\mathop \smallint \limits_\Omega \)fvcdx, all v ε X; where X is a suitable Hilbert space contained in H loc 1,1 (Ω). Criteria are given in order that the Green's operator for this problem have an integral representation and bounded eigenfunctions; in addition, criteria for compactness are given.

Keywords

Hilbert Space Elliptic Equation Integral Representation Connected Region Measurable Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • C. V. Coffman
    • 1
  • M. M. Marcus
    • 1
  • V. J. Mizel
    • 1
  1. 1.Pittsburgh

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