通过较低的 $$L^{p}$ 估计值实现非线性准单调系统解的部分正则性

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-06-07 DOI:10.1007/s00030-024-00946-3

Christoph Hamburger

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引用次数: 0

摘要

我们证明了在系数函数 A 和 B 的自然多项式增长下，非线性准正交系统 ${text {div}A\left( x,u,Du\right) +B\left( x,u,Du\right) =0$的解 u 的部分正则性。我们提出了一种新的直接方法，该方法基于具有低指数 $p>1$ 的 $L^{p}$ 估计，适用于具有常数系数的线性椭圆系统。

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Partial regularity of solutions of nonlinear quasimonotone systems via a lower $$L^{p}$$ estimate

We prove partial regularity of solutions u of the nonlinear quasimonotone system ${\text {div}}A\left( x,u,Du\right) +B\left( x,u,Du\right) =0$ under natural polynomial growth of its coefficient functions A and B. We propose a new direct method based on an $L^{p}$ estimate with low exponent $p>1$ for a linear elliptic system with constant coefficient.

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Nonlinear Differential Equations and Applications (NoDEA)

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