Strong Stability Results for Solutions of Elliptic Equations with Power-like Lower Order Terms and Measure Data☆
Strong Stability Results for Solutions of Elliptic Equations with Power-like Lower Order Terms and Measure Data☆
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DOI：
10.1006/jfan.2001.3846
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发表时间：
2002-03
影响因子：
1.7
通讯作者：
L. Orsina;A. Prignet
中科院分区：
文献类型：
--
作者：
L. Orsina;A. Prignet
摘要 设 u n 为 −div(a(x, u n , ∇u n ))+|u n | 的解序列q −1 u n =f n in Ω，u n =0 on ∂Ω，其中 Ω 是 R N 中的有界集，f n 是强收敛于 L 1 loc ( Ω \ K ) 中函数 f 的函数序列，其中 K 是 Ω 中 r 容量为零的紧致；不对集合 K 上的序列 f n 做出任何假设。我们证明，如果 a 相对于 ∇ u ( p >1) 具有 p −1 阶增长，并且如果 q > r ( p −1)/( r − p )，则 u n 收敛于 u ，即与数据 f 相同问题的解，从而将 H. Brezis 的众所周知的结果扩展到非线性情况。
Abstract Let u n be the sequence of solutions of −div(a(x, u n , ∇u n ))+|u n | q −1 u n =f n in Ω, u n =0 on ∂Ω, where Ω is a bounded set in R N and f n is a sequence of functions which is strongly convergent to a function f in L 1 loc ( Ω \ K ), with K a compact in Ω of zero r -capacity; no assumptions are made on the sequence f n on the set K . We prove that if a has growth of order p −1 with respect to ∇ u ( p >1), and if q > r ( p −1)/( r − p ), then u n converges to u , the solution of the same problem with datum f , thus extending to the nonlinear case a well-known result by H. Brezis.