On the range of elliptic, second order, nonvariational operators in Sobolev spaces

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The subfamilyR(p, Ω) of the class of second order, uniformly elliptic, non variational operators L with bounded measurable coefficients, such that L(W2, p (Ω)) is dense in Lp (Ω), is studied. Sufficient and necessary and sufficient conditions are given, for L to belong toR(p, Ω). An operator L of the class above and not inR(p, Ω) is constructed.


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Entrata in Redazione il 5 ottobre 1998.

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Manselli, P. On the range of elliptic, second order, nonvariational operators in Sobolev spaces. Annali di Matematica pura ed applicata 178, 67–80 (2000).

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  • Elliptic Equation
  • Dirichlet Problem
  • Elliptic Operator
  • Adjoint Equation
  • Measurable Coefficient