Full C1,α-regularity for free and constrained local minimizers of elliptic variational integrals¶with nearly linear growth

Abstract:

We consider local minimizers of elliptic variational integrals with integrand f of nearly linear growth. In the scalar case N= 1 a side condition of the type u≥Φ may be incorporated, for N > 1 u is an unconstrained minimizer and f is required just to depend on the modulus of Du. We show in both cases that u has Hölder continuous first derivatives in the interior of the domain Ω.