退化广义方程的各向异性高阶半正则性
Anisotropic Higher-Order Semiregularity of Degenerate Generalized Equations
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中文总结 AI 辅助
该研究针对退化广义方程，建立了光滑映射与广义方程的各向异性高阶覆盖及逆估计的三角形式化，提出含闭凸过程内近似的满射准则，为集值分析提供了定标包含关系。
中文摘要 AI 辅助
我们针对光滑映射与广义方程，给出了各向异性高阶覆盖与逆估计的自包含三角形式化表述。对于一个映至有限维目标空间的$C^p$映射，我们固定一个索引化的目标分解，施加对应的三角因子条件，并选取满足相关三角$p$-核条件的方向。所得三角$p$-因子算子的满射性给出了一个定标包含关系，其中每个非零块$Y_i$按阶$t^i$被覆盖，因此在该块上具有指数为$1/i$的逆估计。允许存在零块，$p$表示最高活动阶次。该光滑结果是一个导数级的阶次形式化：它直接从$C^p$导数验证模型，并记录集值分析所需的分块定标包含关系。对于广义方程，一个辅助精确模型定理通过无环修正纤维分离出值域转移机制。主要充分准则采用闭凸过程的内近似，其与光滑三角因子算子的和为满射，允许集值项补充缺失方向。
英文摘要
We give a self-contained triangular formulation of anisotropic higher-order covering and inverse estimates for smooth mappings and generalized equations. For a $C^p$ mapping into a finite-dimensional target, an indexed target decomposition is fixed, the corresponding triangular factor condition is imposed, and a direction satisfying the associated triangular $p$-kernel condition is chosen. Surjectivity of the resulting triangular $p$-factor operator yields a fixed-scale inclusion in which each nonzero block $Y_i$ is covered at order $t^i$, and hence an inverse estimate with exponent $1/i$ on that block. Zero blocks are allowed, and $p$ denotes the highest active grade. The smooth result is a derivative-level graded formulation: it verifies the model directly from the $C^p$ derivatives and records the blockwise fixed-scale inclusion needed for the set-valued analysis. For generalized equations, an auxiliary exact-model theorem isolates the range-transfer mechanism with acyclic correction fibres. The main sufficient criterion uses a closed convex-process inner approximation whose sum with the smooth triangular factor operator is surjective, allowing the set-valued term to supply missing directions.
