The authors state appropriate growth conditions to be imposed on the function to ensure that a local minimizer of the functional (1) satisfies certain local boundedness conditions. Here is a bounded open set in and is defined on . It is assumed that satisfies
where , , , if or any if , all summations extend over , and is a non-negative function in , where . Let , then if satisfies (2) and if is a local minimizer of (1) then . The authors also consider the functional (3) , where is now a function from to satisfying
for any , where if ( if ) and , . Then if is a local minimizer of (3) and satisfies (4), (5) then .