Steklov eigenvalue problem
E910281
The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Steklov eigenvalue problem canonical | 1 |
| Steklov eigenvalues | 1 |
| Steklov problem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11186002 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Steklov eigenvalue problem Context triple: [Vladimir Steklov, notableFor, Steklov eigenvalue problem]
-
A.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
B.
Dirichlet problem
The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
-
C.
Morawetz inequalities
Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
-
D.
Neumann boundary conditions in potential theory
Neumann boundary conditions in potential theory specify that the normal derivative of a potential function on a boundary is prescribed, modeling situations where flux across the boundary is controlled rather than the potential itself.
-
E.
Noether boundary value problems
Noether boundary value problems are a class of boundary value problems in the theory of partial differential equations characterized by conditions ensuring well-posedness and finite-dimensional solution spaces, developed by mathematician Fritz Noether.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Steklov eigenvalue problem Target entity description: The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
-
A.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
B.
Dirichlet problem
The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
-
C.
Morawetz inequalities
Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
-
D.
Neumann boundary conditions in potential theory
Neumann boundary conditions in potential theory specify that the normal derivative of a potential function on a boundary is prescribed, modeling situations where flux across the boundary is controlled rather than the potential itself.
-
E.
Noether boundary value problems
Noether boundary value problems are a class of boundary value problems in the theory of partial differential equations characterized by conditions ensuring well-posedness and finite-dimensional solution spaces, developed by mathematician Fritz Noether.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
eigenvalue problem
ⓘ
spectral boundary value problem ⓘ |
| definedOn |
Riemannian manifold with boundary
ⓘ
bounded domain ⓘ |
| eigenvaluesOf | Dirichlet-to-Neumann operator NERFINISHED ⓘ |
| hasApplication |
determining boundary behavior of harmonic functions
ⓘ
spectral characterization of domain geometry ⓘ |
| hasBoundaryCondition | ∂u/∂n = σ u on ∂Ω ⓘ |
| hasEquation | Δu = 0 in Ω ⓘ |
| hasFeature |
discrete spectrum under suitable conditions
ⓘ
eigenvalues appear in boundary conditions ⓘ orthogonal eigenfunctions with respect to suitable inner product ⓘ real eigenvalues for self-adjoint realizations ⓘ self-adjoint operator ⓘ spectral parameter in boundary condition ⓘ |
| hasGeneralization |
biharmonic Steklov problem
NERFINISHED
ⓘ
nonlinear Steklov problem NERFINISHED ⓘ weighted Steklov problem ⓘ |
| hasHistoricalPeriod | early 20th century ⓘ |
| hasKeyConcept |
boundary spectral data
ⓘ
normal derivative on boundary ⓘ trace of harmonic functions ⓘ |
| hasOperator | Dirichlet-to-Neumann operator NERFINISHED ⓘ |
| hasProperty |
eigenfunctions form a basis under suitable conditions
ⓘ
eigenvalues depend on domain geometry ⓘ eigenvalues scale with boundary measure under rescaling ⓘ invariant under isometries of the domain ⓘ |
| hasSpectrum |
0 = σ₀ ≤ σ₁ ≤ σ₂ ≤ …
ⓘ
sequence of Steklov eigenvalues ⓘ |
| hasUnknown |
eigenfunction u
ⓘ
eigenvalue σ ⓘ |
| involves |
boundary conditions
ⓘ
partial differential equations ⓘ |
| namedAfter | Vladimir Andreevich Steklov NERFINISHED ⓘ |
| relatedTo |
Dirichlet boundary value problem
NERFINISHED
ⓘ
Laplace eigenvalue problem NERFINISHED ⓘ Neumann boundary value problem NERFINISHED ⓘ Robin boundary value problem ⓘ |
| studiedIn |
PDE theory
ⓘ
spectral theory of elliptic operators ⓘ |
| usedIn |
fluid–structure interaction models
ⓘ
geometric analysis ⓘ inverse problems ⓘ mathematical physics ⓘ shape optimization ⓘ spectral geometry ⓘ vibration analysis with boundary mass or impedance ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Steklov eigenvalue problem Description of subject: The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Steklov problem
this entity surface form:
Steklov eigenvalues