Dirichlet energy information

the Dirichlet energy is a measure of how variable a function is. More abstractly, it is a quadratic functional on the Sobolev space H1. The Dirichlet energy...

Johann Peter Gustav Lejeune Dirichlet (German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number theory, he proved...

also arises as the Euler-Lagrange equation of a functional called the Dirichlet energy. As such, the theory of harmonic maps contains both the theory of unit-speed...

In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region...

points of a generalized Dirichlet energy functional (this includes harmonic functions as a special case, a result known as Dirichlet principle). This kind...

Laplacian can be defined wherever the Dirichlet energy functional makes sense, which is the theory of Dirichlet forms. For spaces with additional structure...

In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can...

tessellation, Dirichlet cell, Dirichlet polygon also called a Voronoi diagram (geometry) Dirichlet's test (analysis) Dirichlet's energy Pigeonhole principle/Dirichlet's...

commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the...

Given α ∈ Ω k ( M ) {\displaystyle \alpha \in \Omega ^{k}(M)} , its Dirichlet energy is E D ( α ) := 1 2 ⟨ ⟨ d α , d α ⟩ ⟩ + 1 2 ⟨ ⟨ δ α , δ α ⟩ ⟩ {\displaystyle...

Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons...

{R} ^{3}} is minimal if and only if it is a critical point of the Dirichlet energy for all compactly supported variations, or equivalently if any point...

be taken as being purely the kinetic energy of a point particle; as a field, this is just the Dirichlet energy in Euclidean space. In two spatial dimensions...

higher-dimensional Poincaré inequalities that provide best constants for the Dirichlet energy of an n-dimensional membrane. Specifically, π is the greatest constant...

mathematical formulation of the problem is to seek minimizers of the Dirichlet energy functional, J = ∫ D | ∇ u | 2 d x {\displaystyle J=\int _{D}|\nabla...

proved a certain "energy quantization," meaning that the defect between the Dirichlet energy of u(T) and the limit of the Dirichlet energy of u(t) as t approaches...

which is often referred to as the "energy" of the function u ( x ) {\displaystyle u(x)} . More generally, a Dirichlet form is a Markovian closed symmetric...

Characteristic energy - Conservation of energy - Consol Energy Dark energy - Decay energy - Direct Energy - Dirichlet's energy - Dyson's sphere - Ecological energetics...

has a variational characterization: C(Σ, S) is the infimum of the Dirichlet's energy functional I [ v ] = 1 ( n − 2 ) σ n ∫ D | ∇ v | 2 d x {\displaystyle...

functions. With this approach, the objective function becomes the Dirichlet energy on u and v: min u , v ∫ S | | ∇ u | | 2 + | | ∇ v | | 2 d A {\displaystyle...

Rivière, T. (February 2003). "Weak density of smooth maps for the Dirichlet energy between manifolds". Geometric and Functional Analysis. 13 (1): 223–257...

applications to the subject of variational inequalities. By adapting the Dirichlet energy, it is standard to recognize solutions of certain wave equations as...

1\leq p<\infty } by minimization of the discrete p {\displaystyle p} -Dirichlet energy functional E ( f )   :=   1 p ∑ x i ∈ V ‖ ∇ w f ( x i , ⋅ ) ‖ ℓ p p...

of the original developers of deep belief networks and of hierarchical Dirichlet processes. Teh was a keynote speaker at Uncertainty in Artificial Intelligence...

to any sums over an arithmetic function f(n). Such sums are known as Dirichlet series. The regularized form f ~ ( s ) = ∑ n = 1 ∞ f ( n ) n − s {\displaystyle...