AI 中文总结
本文针对有界Lipschitz区域内满足余法边界条件的一类非线性椭圆方程弱解，利用Morrey空间理论等方法推导其一致先验界，关键在于构造相关测度并应用Hartman-Stampacchia引理实现边界控制。
AI 中文摘要
我们研究有界Lipschitz区域中一类满足余法边界条件的非线性椭圆方程弱解的全局有界性。运用Morrey空间理论、Adams-Mazya迹不等式以及梯度的高阶可积性性质，我们推导了解的一致先验界。分析中的关键步骤是构造与解相关的合适测度，并应用Hartman-Stampacchia引理，该引理使我们能够控制解直至区域边界。
英文摘要
We study the global boundedness of weak solutions to a class of nonlinear elliptic equations in bounded Lipschitz domains, subject to conormal boundary conditions. Using techniques from Morrey space theory, Adams--Mazya trace inequalities, and higher integrability properties of the gradient, we derive uniform a priori bounds for the solutions. A crucial step in our analysis is the construction of appropriate measures associated with the solution and the application of the Hartman--Stampacchia lemma, which enables us to control the solution up to the boundary of the domain.
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