In mathematics, a Sobolev mapping is a mapping between manifolds which has smoothness in some sense.
Sobolev mappings appear naturally in manifold-constrained problems in the calculus of variations and partial differential equations, including the theory of harmonic maps.
In mathematics, a Sobolevmapping is a mapping between manifolds which has smoothness in some sense. Sobolevmappings appear naturally in manifold-constrained...
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its...
Prof Sergei Lvovich Sobolev, FRSE (Russian: Серге́й Льво́вич Со́болев; 6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical...
data Spline – Mathematical function defined piecewise by polynomials Sobolevmapping Weisstein, Eric W. "Smooth Function". mathworld.wolfram.com. Archived...
1007/BF01236935 Malý, J; Swanson, D; Ziemer, W (2002), "The co-area formula for Sobolevmappings" (PDF), Transactions of the American Mathematical Society, 355 (2):...
the theory of Sobolev spaces for planar domains or from classical potential theory. Other methods for proving the smooth Riemann mapping theorem include...
is in the Sobolev space W1,2(D) and satisfies the corresponding Beltrami equation (1) in the distributional sense. As with Riemann's mapping theorem, this...
is understood in terms of the spectral mapping theorem. Apart from providing a workable definition of Sobolev spaces for non-integer s, this definition...
measured via the Sobolev norm on spatial derivatives of the flow of vector fields. The large deformation diffeomorphic metric mapping (LDDMM) code that...
In mathematics, Sobolev spaces for planar domains are one of the principal techniques used in the theory of partial differential equations for solving...
the Kinetic energy of the flow. The kinetic energy is defined through a Sobolev smoothness norm with strictly more than two generalized, square-integrable...
continuous mappings from the circle to M , {\displaystyle M,} that is, the free loop space of M . {\displaystyle M.} The Sobolev kind mapping space L ...
which is Dirichlet's principle, representing harmonic functions in the Sobolev space H1(Ω) as the minimizers of the Dirichlet energy integral J ( u )...
strongly Lipschitz domain is given by the two-bricks domain Many of the Sobolev embedding theorems require that the domain of study be a Lipschitz domain...
{R} )} compact support in limit topology W k , p {\displaystyle W^{k,p}} Sobolev space of functions whose weak derivatives up to order k are in L p {\displaystyle...
Hilbert space approach through Sobolev spaces does yield such information. The solution of the Dirichlet problem using Sobolev spaces for planar domains can...
neural networks, marking a departure from the typical focus on learning mappings between finite-dimensional Euclidean spaces or finite sets. Neural operators...
inequality is true. In such spaces the differential calculus goes a long way: Sobolev spaces, differentiation theorems, Hardy spaces. It is noticeable that in...
delta function defines a bounded linear functional. The Sobolev embedding theorem for Sobolev spaces on the real line R implies that any square-integrable...
Borel functional calculus Hilbert–Pólya conjecture Lp space Hardy space Sobolev space Tsirelson space ba space Uniform norm Matrix norm Spectral radius...
precursor of the modern theory of elliptic differential operators and Sobolev spaces. These techniques were originally applied to prove the uniformization...
J. Duchon, 1976, Splines minimizing rotation invariant semi-norms in Sobolev spaces. pp 85–100, In: Constructive Theory of Functions of Several Variables...
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