It is well known that for an elliptic equation of m-th order denned in a bounded domain, the solution is in Ok+m’i'f if the right hand side is in 0*+7, where Ok+y function means a function in Ok class, and all it...It is well known that for an elliptic equation of m-th order denned in a bounded domain, the solution is in Ok+m’i'f if the right hand side is in 0*+7, where Ok+y function means a function in Ok class, and all its k-ih derivatives satisty Holder condition with index y(0<7<.) (see [1]). This conclusion does not work in the critical cases 7=0, 1. This paper is devoted to study the 'smoothness gain' of solutions in these critical cases. Our technique stems from [2], and the more delicate analysis offers us the finer results.展开更多
文摘It is well known that for an elliptic equation of m-th order denned in a bounded domain, the solution is in Ok+m’i'f if the right hand side is in 0*+7, where Ok+y function means a function in Ok class, and all its k-ih derivatives satisty Holder condition with index y(0<7<.) (see [1]). This conclusion does not work in the critical cases 7=0, 1. This paper is devoted to study the 'smoothness gain' of solutions in these critical cases. Our technique stems from [2], and the more delicate analysis offers us the finer results.
