Global Hölder Regularity for Nonlinear Nonvariational Elliptic Systems

Mario MARINO

Dipartimento di Matematica e Informatica, Università di Catania

Viale A. Doria, 6 – 95125 CATANIA (ITALIA)

          e-mail: mmarino@dmi.unict.it

Antonino MAUGERI

Dipartimento di Matematica e Informatica, Università di Catania

Viale A. Doria, 6 – 95125 CATANIA (ITALIA)

          e-mail: maugeri@dmi.unict.it

Abstract. We present a theory of global regularity for the strong solutions u to the Dirichlet problem for nonvariational nonlinear elliptic systems of Carathéodory type. The main result is that the global regularity holds only for low values of dimensions, for istance u is Hölder continuous on \overline{Ω} for n ≤ 6, Du for n ≤ 4 and D^{2}u for n ≤ 2.