带权高阶椭圆方程正解的退化性与正则性  

Decay and regularity of positive solutions for a weighted high-order elliptic equation

作　　者：李冬艳[1] 陆玲 LI Dongyan;LU Ling(School of Science, Xi’an Polytechnic University, Xi’an 710048, China;T&R Office of Mathematics, Army Academy of Border and Coastal Defence, Xi’an 710108,China)

机构地区：[1]西安工程大学理学院,陕西西安710048 [2]陆军边海防学院数学教研室,陕西西安710108

出　　处：《纺织高校基础科学学报》2021年第2期81-86,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11801431);陕西高校科协青年人才托举计划(20190509)。

摘　　要：针对一类带有奇异性的高阶半线性椭圆方程正解的奇异退化性与正则性问题,通过Re-scaling变换及Double引理,结合Liouville型定理,建立全空间中带有奇异性高阶椭圆方程正解的奇异退化性估计。利用嵌入结果,研究单位球上具有Navier边值问题方程弱径向对称解的正则性。结果表明:当指数1<p<{minN+4/N-4,p_(s)}时,带有奇异性的高阶半线性椭圆方程正解具有一定的退化性;弱径向对称解具有良好的光滑性。Some singularity and decay estimates of positive solutions for a weighted high-order semilinear elliptic equation are established based on Re-scaling arguments and a Double lemma,combined with Liouville theorem in RN.Moreover,the regularity of weak radial solutions with Navier boundary value problems for a weighted high-order elliptic equation is studied by the embedding results.The results show that when 1<p<min{N+4/N-4,p_(s)},positive solutions with singularity for a weighted high-order elliptic equation has and decay estimates and weak radial solutions are smooth.

关 键 词：Re-scaling变换 奇异性和退化性 正则性 正解 Navier边值 

分 类 号：O175.29[理学—数学]