Dirichlet form

In the branch of mathematics known as potential theory, a Dirichlet form is a generalization of the Laplacian that can be defined on every measure space, without the need for mentioning partial derivatives. This allows mathematicians to study the Laplace equation and heat equation on spaces that are not manifolds: for example, fractals. To accomplish this generalization, one focuses not on the Laplacian itself but on the quantity In the branch of mathematics known as potential theory, a Dirichlet form is a generalization of the Laplacian that can be defined on every measure space, without the need for mentioning partial derivatives. This allows mathematicians to study the Laplace equation and heat equation on spaces that are not manifolds: for example, fractals. To accomplish this generalization, one focuses not on the Laplacian itself but on the quantity