Compactness method

A compactness method refers to any method to construct or control solutions to PDE by exploiting the compactness (or precompactness) of various subsets of a function space in various topologies. Since most sets are not compact in the strong topology, one often has to rely on compactness in fairly weak topologies.

Examples of compactness methods

• Penalization methods
• Variational methods
• Compensated compactness
• Concentration compactness