Annali di Matematica Pura ed Applicata

, Volume 110, Issue 1, pp 223–245

Boundary value problems for nonuniformly elliptic equations with measurable coefficients


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

DOI: 10.1007/BF02418007

Cite this article as:
Coffman, C.V., Marcus, M.M. & Mizel, V.J. Annali di Matematica (1976) 110: 223. doi:10.1007/BF02418007


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 Hloc1,1(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.

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© Fondazione Annali di Matematica Pura ed Applicata 1975