Local boundedness for minima of functionals with nonstandard growth conditions

Abstract

We prove the local boundedness of local minimizers of functionals of the form F(u) = ∫_Ω f(x, u, ∇u) dx , where f satisfies some convexity assumptions and its growth with respect to the gradient is controlled in terms of a Young function of ∆_2 class and its Sobolev conjugate. The results extend some boundedness theorems for minimizers of functionals satisfying the so called p, q-growth conditions.

Keywords

• integral functionals
• nonstandard growth conditions
• minimizers
• local boundedness