设Ω是R^m(m≥2)中一个有界区域,考虑多调和算子组的特征值问题AΛ(△)u^T=λu^T,x∈Ωu^k=(?)u^k/(?)n=…=(?)^(k-1)u^k/(?)n^(k-1)=0,x∈(?)Ω,k=1,2,…,N其中,u=(u^1,u^2,…,u^N),n是(?)Ω的单位外法向量。将特征值按增加的顺序排列...设Ω是R^m(m≥2)中一个有界区域,考虑多调和算子组的特征值问题AΛ(△)u^T=λu^T,x∈Ωu^k=(?)u^k/(?)n=…=(?)^(k-1)u^k/(?)n^(k-1)=0,x∈(?)Ω,k=1,2,…,N其中,u=(u^1,u^2,…,u^N),n是(?)Ω的单位外法向量。将特征值按增加的顺序排列为0<λ_1≤λ_2≤…≤λ_n≤…则成立如下不等式λ_(n+1)≤λ_n+4/m^2n^2(sum from i=1 to n sum from h=1 to N λ_i^(1/k))(sum from i=1 to n sum from k=1 to N k(2k+m-2)λ_i^(1-1/k)) sum from i=1 to n sum from k=1 to N λ_i^(1/k)/λ_(n+1)-λ_i≥m^2n^2/(sum from i=1 to n sum from k=1 to N 4k(2k+m-2)λ_i^(1-1/k))展开更多
This paper introduces a generic eigenvalue flow of a parameter family of operators, where the corresponding eigenfunction is continuous in parameters. Then the author applies the result to the study of polynomial grow...This paper introduces a generic eigenvalue flow of a parameter family of operators, where the corresponding eigenfunction is continuous in parameters. Then the author applies the result to the study of polynomial growth L-harmonic functions. Under the assumption that the operator has some weakly conic structures at infinity which is not necessarily unique, a Harnack type uniform growth estimate is obtained.展开更多
基金This project is Supported partially by the Research Funds for Doctoral Programs at Higher Educational Institutions and Nation Science Fund of China.
文摘设Ω是R^m(m≥2)中一个有界区域,考虑多调和算子组的特征值问题AΛ(△)u^T=λu^T,x∈Ωu^k=(?)u^k/(?)n=…=(?)^(k-1)u^k/(?)n^(k-1)=0,x∈(?)Ω,k=1,2,…,N其中,u=(u^1,u^2,…,u^N),n是(?)Ω的单位外法向量。将特征值按增加的顺序排列为0<λ_1≤λ_2≤…≤λ_n≤…则成立如下不等式λ_(n+1)≤λ_n+4/m^2n^2(sum from i=1 to n sum from h=1 to N λ_i^(1/k))(sum from i=1 to n sum from k=1 to N k(2k+m-2)λ_i^(1-1/k)) sum from i=1 to n sum from k=1 to N λ_i^(1/k)/λ_(n+1)-λ_i≥m^2n^2/(sum from i=1 to n sum from k=1 to N 4k(2k+m-2)λ_i^(1-1/k))
文摘This paper introduces a generic eigenvalue flow of a parameter family of operators, where the corresponding eigenfunction is continuous in parameters. Then the author applies the result to the study of polynomial growth L-harmonic functions. Under the assumption that the operator has some weakly conic structures at infinity which is not necessarily unique, a Harnack type uniform growth estimate is obtained.
