Abstract
Regularity results in domains of Euclidean n-space are established for generalized solutions of second order elliptic equations for which the coefficients of the differential operator and the nonhomogeneous term satisfy a Dini criterion. Generalized solutions are shown to be essentially classical solutions and a bound for the modulus of continuity of second order partial derivatives of the solution is established which yields Weyl's lemma as a corollary. A differentiability theorem is also established for the case the terms of the equation have further differentiability properties.
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