Editing Partial differential equation (section)

=== Regularity ===
{{Main|Regularity theory}}
Regularity refers to the integrability and differentiability of weak solutions, which can often be represented by [[Sobolev space|Sobolev spaces]]. 

This problem arise due to the difficulty in searching for classical solutions. Researchers often tend to find weak solutions at first and then find out whether it is smooth enough to be qualified as a classical solution.

Results from [[functional analysis]] are often used in this field of study.