A proof of the Cp′-regularity conjecture in the plane
A proof of the Cp′-regularity conjecture in the plane
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DOI：
10.1016/j.aim.2017.06.027
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发表时间：
2017-08
影响因子：
1.7
通讯作者：
Damiao J. Ara'ujo;E. Teixeira;J. M. Urbano
中科院分区：
文献类型：
--
作者：
Damiao J. Ara'ujo;E. Teixeira;J. M. Urbano
本文建立了一类非线性椭圆型退化偏微分方程解的一个新的振动估计。这个新的工具产生一个精确的控制的增长速度的解决方案附近的一组临界点，椭圆退化。因此，我们能够证明长期存在的猜想的平面对应物，即具有有界源的退化p-Poisson方程的解局部属于类C p′= C 1，1 p− 1;这种正则性是最优的。
We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C p′= C 1, 1 p− 1; this regularity is optimal.