一类完全非线性椭圆偏微分方程的Schauder估计：几何切向方法
Schauder estimates for a class of fully nonlinear elliptic PDEs: a geometric tangential approach
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中文总结 AI 辅助
本文通过爆破论证、几何切向分析与紧致性技术，为非凸非凹完全非线性椭圆PDE的经典解建立了局部与全局Schauder估计。
中文摘要 AI 辅助
本文在数据满足适当Hölder连续性的假设下，为一类不一定凸或凹的完全非线性椭圆偏微分方程经典解建立了局部和全局Schauder估计。我们的方法基于稳健的爆破论证，结合几何切向分析和紧致性技术。该策略深受当代非线性椭圆偏微分方程理论中发展出的方法论影响。
英文摘要
In this paper, we establish local and global Schauder estimates for classical solutions of a class of fully nonlinear elliptic partial differential equations, which are not necessarily convex or concave, under suitable Hölder continuity assumptions on the data. Our approach is based on a robust blow-up argument, combined with geometric tangential analysis and compactness techniques. This strategy is strongly influenced by methodologies developed in the contemporary theory of nonlinear elliptic PDEs.
发表机构
- Universidade Estadual de Campinas（坎皮纳斯州立大学）
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