Local boundedness under nonstandard growth conditions

Abstract

This paper deals with local boundedness under nonstandard growth conditions by using De Giorgi's iteration method. We first consider quasilinear elliptic systems, and assume that the coefficients satisfying some boundedness and coercivity conditions, then we derive local boundedness of solutions. Secondly, we consider elliptic equations with a drift term, under some nonstandard growth conditions, we derive that solutions are locally bounded. Finally, we consider variational integrals with the integrand satisfy nonstandard growth conditions, local boundedness of minimizers is derived.