Elliptic Systems, Singular Sets and Dini Continuity Frank Duzaar, 1, * Andreas Gastel, 1 and Giuseppe Mingione 2 1 Mathematisches Institut der Friedrich-Alexander-Universita ¨t, Erlangen-Nu ¨ rnberg, Erlangen, Germany 2 Dipartimento di Matematica, Universita ` di Parma, Parma, Italy ABSTRACT We estimate the size of the singular set of solutions to non-linear elliptic systems of the form div aðx; u; DuÞ¼ bðx; u; DuÞ where the vector field a satisfies a Dini-type continuity condition with respect to the variables ðx; uÞ. Key Words: Elliptic systems; Singular set; Hausdorff dimension; Dini continuity. Mathematics Subject Classification: 35J60; 35D10. *Correspondence: Frank Duzaar, Mathematisches Institut der Friedrich-Alexander- Universita ¨t, Erlangen-Nu ¨rnberg, Bismarckstr. 11=2, 91054 Erlangen, Germany; Fax: +49-9131- 8522081; E-mail: duzaar@mi.uni-erlangen.de. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS Vol. 29, Nos. 7 & 8, pp. 1215–1240, 2004 1215 DOI: 10.1081/PDE-200033734 0360-5302 (Print); 1532-4133 (Online) Copyright # 2004 by Marcel Dekker, Inc. www.dekker.com