论文标题
车道填充完全非线性类型系统和应用的主要光谱曲线
Principal spectral curves for Lane-Emden fully nonlinear type systems and applications
论文作者
论文摘要
在本文中，我们利用了具有可能无限的系数和权重的完全非线性泳道类型系统的背景下，两个主要半特征值的现象。我们表明，这导致了平面上存在两个主要光谱曲线。我们还构建了与第二个特征值和反量最大原理有关的可能的第三频谱曲线，即使对于涉及线性运算符的车道填充系统，这些曲线都是新颖的。作为应用，我们在这些系统的小域中得出了最大原理，以及在均方根状态中正溶液的存在和唯一性。即使在标量情况下，我们的大多数结果都是新的，特别是对于Isaac的一类具有无限系数的运营商，其$ w^{2，\ varrho} $规则性估计我们也证明。
In this paper we exploit the phenomenon of two principal half eigenvalues in the context of fully nonlinear Lane-Emden type systems with possibly unbounded coefficients and weights. We show that this gives rise to the existence of two principal spectral curves on the plane. We also construct a possible third spectral curve related to a second eigenvalue and an anti-maximum principle, which are novelties even for Lane-Emden systems involving linear operators. As applications, we derive a maximum principle in small domains for these systems, as well as existence and uniqueness of positive solutions in the sublinear regime. Most of our results are new even in the scalar case, in particular for a class of Isaac's operators with unbounded coefficients, whose $W^{2,\varrho}$ regularity estimates we also prove.
