Elliptic boundary value problem with superposition operator in the boundary value condition. II.
type: Item
instance of: scholarly article
title: Elliptic boundary value problem with superposition operator in the boundary value condition. II.
zbMATH Open document ID: 1103.35026
author: A. K. Ratyni
published in: Russian Mathematics
publication date: 2003-07-30T00:00:00Z
review text: The article continues previous work of the author [Part I, Russ. Math. 44, No. 4, 34--38 (2000); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2000, No. 4, 36--40 (2000; Zbl 0965.35032)] where the Bitsadze--Samarskii problem \[ {\mathcal L}u\equiv \sum_{i,j=1}^n a_{ij}(x)u_{x_ix_j} + \sum_{i=1}^n b_{i}(x)u_{x_i}+c(x)u=f(x)\qquad x\in D\subset {\mathbb R}^n, \] \[ {\mathcal B}u\equiv u(x)-u(\sigma x)=\psi(x)\qquad x\in S=\partial D \] was considered under the assumption that the set \(\sigma S \cap S\equiv \omega\) is nonempty and \(\sigma\omega\subset\omega.\) Here the problem is studied without these constraints on \(\sigma.\) Precisely, the solvability theory depends essentially on the iterates of the mapping \(\sigma,\) that is, whether \(\sigma\) generates the ``absorbing set'' \( \Omega\equiv \left\{x\in S: \sigma^i x\in S,\;i=1,2,\ldots\right\}\) on \(S\).
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1956410
zbMATH Keywords: superposition operator
zbMATH Keywords: nonlinear boundary condition
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1956410