A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems
type: Item
instance of: scholarly article
title: A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems
zbMATH Open document ID: 1479.65038
author: Kouta Sekine
author: Mitsuhiro T. Nakao
author: Shin'ichi Oishi
author: Masahide Kashiwagi
published in: Applied Numerical Mathematics
publication date: 2021-08-05T00:00:00Z
Mathematics Subject Classification ID: 65N99
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 68V05
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 7379320
zbMATH Keywords: non-existence proof
zbMATH Keywords: numerical proof
zbMATH Keywords: computer-assisted proof
zbMATH Keywords: elliptic problems
describes a project that uses: kv
MaRDI profile type: Publication
full work available at URL: j.apnum.2021.06.011
OpenAlex ID: W3175250000
cites work: Q5601657
cites work: Q2765612
cites work: Q4448960
cites work: Interval analysis and automatic result verification
cites work: A Test for Existence of Solutions to Nonlinear Systems
cites work: Safe Starting Regions for Iterative Methods
cites work: Introduction to Interval Analysis
cites work: A numerical approach to the proof of existence of solutions for elliptic problems
cites work: A numerical approach to the proof of existence of solutions for elliptic problems II
cites work: NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
cites work: An efficient approach to the numerical verification for solutions of elliptic differential equations
cites work: A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems
cites work: Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
cites work: Numerical verification of existence and inclusion of solutions for nonlinear operator equations
cites work: Bounds for eigenvalues of second-order elliptic differential operators
cites work: Q4364444
cites work: Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance
cites work: Computer-assisted proofs for semilinear elliptic boundary value problems
cites work: A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator
cites work: Sharp numerical inclusion of the best constant for embedding \(H_0^1(\Omega) \hookrightarrow L^p(\Omega)\) on bounded convex domain
cites work: Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces
cites work: A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
cites work: Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element
DOI: 10.1016/J.APNUM.2021.06.011
description: scientific article; zbMATH DE number 7379320