The concept of regularity concerns the smoothness of weak solutions to partial differential equations.
Regularity is used to demonstrate the smoothness of weak solutions to partial differential equations. This theory is used for elliptic, parabolic, and hyperbolic PDEs.
Assuming that PDE solution defined on its domain is smooth on the boundary, the goal is to demonstrate that the same solution is also smooth on the interior of the domain. Then the solution is also differentiable at least once. Furthermore, higher regularity is utilized to establish that the solution is differentiable more than once, including infinitely many times.