A boundary estimate for nonlinear equations with discontinuous coefficients

Juha Kinnunen; Shulin Zhou

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A boundary estimate for nonlinear equations with discontinuous coefficients

机译：具有不连续系数的非线性方程的边界估计

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摘要

We prove a boundary estimate for the gradient of a weak solution to a partial differential equation of p-Laplacian type with coefficients of vanishing mean oscillation. Combining the boundary estimate with a known interior estimate we obtain a global higher integrability result. The main result generalizes known results for linear equations to a nonlinear case. Our method is based on choosing the right test function, and, in particular, we do not use any representation formulas for solutions.

机译：我们证明了p-Laplacian型偏微分方程的弱解的梯度的边界估计，该系数具有消失的平均振荡系数。将边界估计与已知的内部估计相结合，我们可以获得全局更高的可积性结果。主要结果将线性方程的已知结果推广到非线性情况。我们的方法是基于选择正确的测试函数的，尤其是，我们不使用任何表示公式来求解。

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来源
《Differential and integral equations》 |2001年第4期|共18页
作者
Juha Kinnunen; Shulin Zhou;
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正文语种 eng
中图分类微分方程、积分方程;
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专利

1. A boundary estimate for nonlinear equations with discontinuous coefficients [J] . Juha Kinnunen, Shulin Zhou Differential and integral equations . 2001,第4期

机译：具有不连续系数的非线性方程的边界估计
2. Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients [J] . Minam Moon, Hyung Kyu Jun, Tay Suh Advances in Mathematical Physics . 2017,第Pta1期

机译：非线性系数抛物面方程杂交不连续Galerkin方法的估计
3. A local estimate for nonlinear equations with discontinuous coefficients [J] . Juha Kinnunen, Shulin Zhou Communications in Partial Differential Equations . 1999,第11a12期

机译：具有不连续系数的非线性方程的局部估计
4. Accuracy Estimates of Difference Schemes for Quasi-Linear Elliptic Equations with Variable Coefficients Taking into Account Boundary Effect [C] . Volodymyr Makarov, Lyubomyr Demkiv International Conference on Numerical Analysis and Its Applications . 2005

机译：考虑边界效应的变系数拟线性椭圆方程的差分方案的精度估计
5. Uniform estimates for the Zakharov system and the initial-boundary value problem for the Korteweg-de Vries and nonlinear Schroedinger equations. [D] . Holmer, Justin Alexander. 2004

机译：Zakharov系统的统一估计以及Korteweg-de Vries和非线性Schroedinger方程的初边值问题。
6. Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients [O] . Kelin Xia, Meng Zhan, Decheng Wan, -1

机译：具有不连续系数的椭圆方程的自适应变形网状界面方法
7. Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients [O] . Minam Moon, Hyung Kyu Jun, Tay Suh 2017

机译：具有非线性系数的抛物面方程杂交不连续Galerkin方法的误差估计

A boundary estimate for nonlinear equations with discontinuous coefficients

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