The asymptotic shift for the principal eigenvalue for second order elliptic operators in the presence of small obstacles
type: Item
instance of: scholarly article
title: The asymptotic shift for the principal eigenvalue for second order elliptic operators in the presence of small obstacles
zbMATH Open document ID: 1172.35044
author: Iddo Ben-Ari
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: The author considers an elliptic second order differential operator \(L\) of the form \[ L = \tfrac{1}{2} \,\nabla \cdot a \nabla + b \nabla + V, \] where \(a = [a_{i j}]_{i,j= 1}^{d} \in C^{2,d} (\mathbb{R}^{d})\) is uniformly elliptic on \(\mathbb{R}^{d}, \;\;b = (b_{1},...,b_{\alpha}) \in C^{1,\alpha} (\mathbb{R}^{d})\) and \(V \in C^{\alpha} (\mathbb{R}^{d}) \;\;\;(\alpha \in (0,1)).\) For a smooth compact domain \(D\) in \(\mathbb{R}^{d}\) it is imposed on \(\partial D\) either Dirichlet or an oblique-derivative boundary condition. The main purpose of the paper is to give asymptotic formulas for the principal eigenvalue of \(L\) under hard and soft obstacle type perturbations.
reviewed by: Petru A. Cojuhari
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 5508739
zbMATH Keywords: elliptic operators
zbMATH Keywords: principal eigenvalue
zbMATH Keywords: asymptotic formulas
zbMATH Keywords: obstacle type perturbations
MaRDI profile type: Publication
full work available at URL: s11856-009-0009-x
OpenAlex ID: W1970910620
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DOI: 10.1007/S11856-009-0009-X
description: scientific article; zbMATH DE number 5508739