完全非线性死核系统

非局部死核问题在分支点处的改进正则性

Improved regularity for a nonlocal dead-core problem

本文研究非局部死核问题在分支点处的正则性，提出一种不依赖极大值原理的新策略，在局部框架内分析两相问题，从而获得改进的正则性结果。

关于具有次线性竞争相互作用的椭圆型系统中死核的出现

On the emergence of dead cores in elliptic systems with sublinear competitive interactions

研究具有次线性耦合项的半线性椭圆型系统，利用次线性方程下解有死核及一致赫尔德界的结论，证明竞争型相互作用下解有死核，并应用于多种解，如基态和最小能量变号解。

A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores

We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions are very mild: we assume that the potential is lower semicontinuous, and satisfies a monotonicity condition in a neighborhood of its minimum. As a consequence, we give a sufficient condition for the existence of dead core regions, where the minimizer is equal to one of the minima of the potential.

不定椭圆问题中死核解的多重性

Multiplicity of dead core solutions in indefinite elliptic problems

本文研究一类带不定系数的次齐次p-Laplace方程，利用死核形成性质证明当参数μ足够大时存在多个非负死核解，并结合唯一性得到精确多重性结果，进而推广到更一般的问题类。

Non-existence of dead cores in fully nonlinear elliptic models

We investigate non-existence of nonnegative dead-core solutions for the problem $$|Du|^γF(x, D^2u)+a(x)u^q = 0 \quad \mbox{in} \quad Ω, \quad u=0 \quad \mbox{ on } \quad \partialΩ.$$ Here $Ω\subset \mathbb{R}^N$ is a bounded smooth domain, $F$ is a fully nonlinear elliptic operator, $a: Ω\to \mathbb{R}$ is a sign-changing weight, $γ\geq 0$, and $0<q<γ+1$. We show that this problem has no non-trivial dead core solutions if either $q$ is close enough to $γ+1$ or the negative part of $a$ is sufficiently small. In addition, we obtain the existence and uniqueness of a positive solution under these …

退化或奇异全非线性死核系统及Hénon型方程的正则性估计改进

Improved regularity estimates for degenerate or singular fully nonlinear dead-core systems and Hénon-type equations

本文研究退化或奇异全非线性死核系统与强吸收项的耦合问题，提出粘性解在自由边界处的正则性提升、非退化性、自由边界测度估计、Liouville型结果及解的发散行为，同时推导了退化权重和强吸收下Hénon型方程粘性解的精确正则性估计。