给出经典Hölder不等式的一个推广,并应用推广的Hölder不等式,研究在边界值不为零的情况下,非线性散度型椭圆方程的边值问题.利用Stampacchia引理以及Sobolev空间的分析技巧,得到解的正则性结果.
A generalization of the classical Hölders inequality is given, which is applied to the study the boundary value problems of nonlinear divergence type elliptic equation when the boundary value is not zero. The regularity property of the solution is obtained by using Stampacchia lemma and the technique of Sobolev spaces.
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