A posteriori verification of the positivity of solutions to elliptic boundary value problems
From MaRDI portal
Publication:2077122
DOI10.1007/S42985-021-00143-2zbMath1485.35165arXiv2011.04510OpenAlexW3194310975WikidataQ114216463 ScholiaQ114216463MaRDI QIDQ2077122
Publication date: 22 February 2022
Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2011.04510
Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bifurcation and symmetry breaking for a class of semilinear elliptic equations in an annulus
- A framework of verified eigenvalue bounds for self-adjoint differential operators
- Sharp numerical inclusion of the best constant for embedding \(H_0^1(\Omega) \hookrightarrow L^p(\Omega)\) on bounded convex domain
- On a maximum principle for weak solutions of some quasi-linear elliptic equations
- On the Schrödinger equation and the eigenvalue problem
- A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions
- Generalized Bessel functions of the first kind
- Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance
- A uniqueness result for a semilinear elliptic problem: a computer-assisted proof
- Symmetry and related properties via the maximum principle
- Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems
- Best constant in Sobolev inequality
- Problèmes isoperimetriques et espaces de Sobolev
- Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle
- Uniqueness of least energy solutions to a semilinear elliptic equation in \(\mathbb{R}^ 2\)
- A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations
- Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation
- Numerical verification method for positive solutions of elliptic problems
- Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains
- Nagumo's equation
- Verified Eigenvalue Evaluation for the Laplacian over Polygonal Domains of Arbitrary Shape
- Numerical verification of positiveness for solutions to semilinear elliptic problems
- A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem
- Validated Continuation for Equilibria of PDEs
- Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
- On the Existence of Positive Solutions of Semilinear Elliptic Equations
- Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
This page was built for publication: A posteriori verification of the positivity of solutions to elliptic boundary value problems
