二阶椭圆方程解的梯度估计

IF 1.5 3区数学 Q1 MATHEMATICS

Advances in Differential Equations Pub Date : 2021-11-22 DOI:10.57262/ade027-0102-77

V. Maz'ya, R. McOwen

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引用次数: 0

摘要

我们得到了一个具有有界可测系数的发散形式的二阶椭圆型方程解的梯度的局部估计，该方程在单点x=0处是平方Dini连续的。特别地，我们处理在x=0处不是Lipschitz连续的解的情况。我们表明我们的估计是准确的。

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Gradient estimate for solutions of second-order elliptic equations

We obtain a local estimate for the gradient of solutions to a second-order elliptic equation in divergence form with bounded measurable coefficients that are square-Dini continuous at the single point x = 0. In particular, we treat the case of solutions that are not Lipschitz continuous at x = 0. We show that our estimate is sharp.

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来源期刊

Advances in Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.