Regularity is a property of
elliptic partial differential equations
Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form
:Au_ + 2Bu_ + Cu_ + Du_x + Eu_y + Fu +G= 0,\,
where ...
such as
Laplace's equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as
\nabla^2\! f = 0 or \Delta f = 0,
where \Delta = \na ...
.
Hilbert's nineteenth problem
Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled in 1900 by David Hilbert. It asks whether the solutions of regular problems in the calculus of variations are always analytic. Informally, and perhaps less ...
was concerned with this concept.
References
Elliptic partial differential equations
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