非光滑k-凸域上或存在子解时的黑塞方程
The Hessian equation on nonsmooth k-convex domains or in the presence of subsolutions
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中文总结 AI 辅助
研究非光滑k-凸域上k-黑塞测度狄利克雷问题，证k>n/2时对特定边界数据有唯一解，严格k-凸域仅需连续边界数据，核心方法未提及，主要贡献是给出狄氏问题解的存在唯一性结论。
中文摘要 AI 辅助
证明了对于k>n/2，在（非光滑且非一致）k-凸（也称为k-超凸）域上，以任何有限博雷尔测度为右侧且边界数据取自该域闭包上的k-凸连续函数的k-黑塞测度的狄利克雷问题有唯一解。对于严格k-凸域，仅连续边界数据就足够了（即存在强障碍时）。
英文摘要
It is proved for $k>n/2$ that the Dirichlet problem of the $k$-Hessian measure on a (nonsmooth and nonuniformly) $k$-convex (also known as $k$-hyperconvex) domain for any finite Borel measure as right-hand side and boundary data taken from a $k$-convex and continuous function on the closure of the domain has a unique solution. Merely continuous boundary data are sufficient for strictly $k$-convex domains (i.e., if there exist strong barriers).
