Compensated compactness: Difference between revisions
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'''Compensated compactness''' is the principle that certain bilinear or nonlinear operators may exhibit good | '''Compensated compactness''' is the principle that certain bilinear or nonlinear operators may exhibit some uenxpectedly good compactness properties | ||
(e.g. mapping bounded sequences to precompact sequences in a suitable strong topology) if they exhibit some cancellation in their | (e.g. mapping bounded sequences to precompact sequences in a suitable strong topology) if they exhibit some cancellation in their | ||
internal structure. It is of particular importance in conservation law equations. For nonlinear dispersive and wave equations, | internal structure. It is of particular importance in conservation law equations. For nonlinear dispersive and wave equations, | ||
Revision as of 19:18, 10 August 2006
Compensated compactness is the principle that certain bilinear or nonlinear operators may exhibit some uenxpectedly good compactness properties
(e.g. mapping bounded sequences to precompact sequences in a suitable strong topology) if they exhibit some cancellation in their
internal structure. It is of particular importance in conservation law equations. For nonlinear dispersive and wave equations,
the counterpart of this principle appears to be the null form estimates. See also concentration compactness, which is another way of salvaging a type of compactness from a non-compact situation.
