On domain of Poisson operators and factorization for divergence form elliptic operators

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• 作者：Yasunori Maekawa ; Hideyuki Miura
• 关键词：Mathematics Subject Classification35J15 ; 35J25
• 刊名：manuscripta mathematica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：152
• 期：3-4
• 页码：459-512
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1785
• 卷排序：152

文摘

We consider second order uniformly elliptic operators of divergence form in \(\mathbb {R}^{d+1}\) whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators related with Poisson operators and Dirichlet–Neumann maps. Consequently, we obtain a solution formula for the inhomogeneous elliptic boundary value problem in the half space, which is useful to show the existence of solutions in a wider class of inhomogeneous data. We also establish \(L^2\) solvability of boundary value problems for a new class of the elliptic operators.