A note on the equilibrium potential of certain Dirichlet spaces

• There exists an equilibrium potential, an element of a Dirichlet space, for any compact subset, with non-emtpy interior, of Rm. This potential is constant on the interior of the set. There is a corresponding measure that is 0 outside the set. We prove that the restriction of this equilibrium measure to the interior of the set is absolutely continuous, and we derive an explicit formula for its density.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Mathematics

Matematik

Publication and Content Type

ref (subject category)

art (subject category)