边际及边界处Carathéodory非线性椭圆方程的一致估计
偏微分方程分析
2025-02-28 v2
摘要
我们建立了关于弱解的略亚临界椭圆问题在内部及边界处同时存在非线性性的显式一致先验估计。我们的显式L^{\infty}(\Omega)先验估计以其H^{1}(\Omega)范数的幂次形式表示。为证明本结果，我们结合了De Giorgi-Nash-Moser迭代方案、椭圆正则性以及Gagliardo-Nirenberg插值不等式。
引用
@article{arxiv.2502.14609,
title = {Uniform estimates for elliptic equations with Carath\'eodory nonlinearities at the interior and on the boundary},
author = {Edgar Antonio and Martín P. Árciga-Alejandre and Rosa Pardo and Jorge Sánchez Ortiz},
journal= {arXiv preprint arXiv:2502.14609},
year = {2025}
}
备注
key words: A priori estimates, slightly subcritical non-linearities, $L^\infty$ a priori bounds, nonlinear boundary conditions