论文标题
用于均匀椭圆方程解决方案的插值不平等
An interpolating inequality for solutions of uniformly elliptic equations
论文作者
论文摘要
我们将作者先前研究中的谐波功能的不平等扩展到以差异形式均匀椭圆方程的解决方案，仅具有可测量的系数。谐波功能的不平等现象是研究Alexandrov的肥皂泡定理和Serrin的问题的径向对称性稳定性的关键要素。我们不平等的证明是基于L. caffarelli的椭圆运算符的平均价值属性，由I. Blank和Z. Hao详细证明。
We extend an inequality for harmonic functions, obtained in previous research by the authors, to the case of solutions of uniformly elliptic equations in divergence form, with merely measurable coefficients. The inequality for harmonic functions turned out to be a crucial ingredient in the study of the stability of the radial symmetry for Alexandrov's Soap Bubble Theorem and Serrin's problem. The proof of our inequality is based on a mean value property for elliptic operators by L. Caffarelli, proved in full detail by I. Blank and Z. Hao.
