一类拟线性椭圆型偏微分方程的先验界的估计(英文)

A Priori Estimates for a Quasilinear Elliptic PDE

英文关键词:estimates  elliptic  queasilinear.

中文摘要:

      近几年对边值问题－ｄｉｖ（｜Ｄｕ｜^p-2Ｄｕ）＝λｆ（ｕ）｝在Ω上ｕ｜(?)Ω＝０正解方面已经得到了许多结果．这里λ＞０，Ω是有界区域和对ｓ≥０，ｆ（ｓ）≥０．在本文中在条件Ｎ≥ｐ＞１，Ω＝Ｂ_１＝｛ｘ∈Ｒ^N，｜ｘ｜＜１｝和ｆ∈Ｃ¹（０，∞）∩Ｃ⁰（［０，∞）），ｆ（０）＝０，研究了这类问题的正对称解的先验界估计．

英文摘要:

      In the recent past many results have been established on positive solutions to boundary value problems of the form - div (|Du(x)|^p-2Du(x))=λf(u(x))} in} Ω, u(x)=0 on (?)Ω,where λ>0, Ω is a bounded smooth domain and f(s)≥ 0 for s≥ 0 . In this paper we study a priori estimates of positive radial solutions of such problems when N>p>1, Ω=B₁={x∈R^N; | x |<1} and f∈C¹(0,∞)∩ C⁰([0,∞)), f(0)=0 .