Local boundedness for solutions of a class of non-uniformly elliptic anisotropic problems

We consider a class of energy integrals, associated to nonlinear and non-uniformly elliptic equations, with integrands f(x,u,ξ) satisfying anisotropic pi,q-growth conditions of the form ∑i=1nλi(x)|ξi|pjavax.xml.bind.JAXBElement@7b04f595≤f(x,u,ξ)≤μ(x)|ξ|q+|u|γ+1 for some exponents γ≥q≥pi>1, and non-negative functions λi,μ subject to suitable summability assumptions. We prove the local boundedness of scalar local quasi-minimizers of such integrals.