Local boundedness for vectorial minimizers of non-uniform variational integrals

We establish the local boundedness of vectorial local minimizers for a specific class of integral functionals with rank-one convex integrands under appropriate structural assumptions. Our method adapts the renowned De Giorgi‘s iteration technique and employs a suitable Caccioppoli-type inequality. Our findings are applicable to polyconvex integrals∫Ω{∑α=1Nλ(x)|Duα|p+μ(x)|Du|r}dx with suitable λ(x),μ(x)>0 and p,r>1.