二阶椭圆方程的下解及Holder连续的一个新证明_英文_.pdfVIP

MATH EMATICA APPLICATA 2010, 23( 4) :724730 * SubsolutionandaNovel Proof of Holders ContinuityforEllipticEquationsof SecondOrder LI Bin( 李彬) , YA NG Han( 杨晗) , SH EN Jie iong( 沈洁琼) ( D ep ar t ment of M ath emati ca l , S out hw est J iaotong Univ er s ity , Che ng d u 610031, Ch ina) Abstract:By using the test funct ions and techni ue of iteration, the paper focus on the subsolution and regularity for elliptic e uations of second order under the w eak smoothness assumption on the coefficients. Furthermore,w e shall give a novel proof of H older s continuity that relies on the local estimate and the Poincare ine uality. Key words:Subsolution; Regularity ; Holder s continuity; Test function; Iteration method; Poincare ine uality CLCNumber:O175. 25 A S(2000)Subject Classification:35J15 Document code:A ArticleID 2010) 1.Introduction T his paper studies linear elliptic operators w ith the principal part in divergence form un der the w eak smoothness assumption on the coefficients. We consider operators L of the form: i i i i i L u = D ( a ( x ) D u + b ( x ) u) + c ( x ) D u + d ( x ) u, ( 1. 1) n w hose coefficients are assumed to be measurable functions on a domain R , and the prin n cipal coefficients are differentiable. We shall assume that L is strictly elliptic in R; that is, there exists a positive number suc