Steklov eigenvalue problem

E910281

eigenvalue problem spectral boundary value problem

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.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (2)

Surface form	Occurrences
Steklov eigenvalues	1
Steklov problem	1

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 ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Vladimir Steklov → notableFor → Steklov eigenvalue problem ⓘ

Vladimir Steklov → hasEponym → Steklov eigenvalue problem ⓘ

this entity surface form: Steklov problem

Vladimir Steklov → hasEponym → Steklov eigenvalue problem ⓘ

this entity surface form: Steklov eigenvalues