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


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.


Hilbert Space Elliptic Equation Integral Representation Connected Region Measurable Coefficient 


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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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