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A Banach or Hilbert space controlling weak derivatives in .
Boundary conditions define important closed subspaces such as .
wp-sobolev_spacenlab-sobolev_spaceEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Sobolev spaces complete functions under norms including weak derivatives.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-sobolev_spacenlab-sobolev_spaceEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Sobolev spaces formulate finite-energy fields and weak solutions of field equations.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
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