Equilibrium points of a singular cooperative system with free boundary

• In this paper we initiate the study of maps minimising the energy integral(D)(vertical bar del u vertical bar(2) + 2 vertical bar u vertical bar) dx, which, due to Lipschitz character of the integrand, gives rise to the singular Euler equations Delta u = u / vertical bar u vertical bar chi({vertical bar u vertical bar >0}), u = (u(1,) ... ,u(m)) Our primary goal in this paper is to set up a road map for future developments of the theory related to such energy minimising maps. Our results here concern regularity of the solution as well as that of the free boundary. They are achieved by using monotonicity formulas and epiperimetric inequalities, in combination with geometric analysis.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Free boundary

Regularity of the singular set

Unique tangent cones

Partial regularity

Publication and Content Type

ref (subject category)

art (subject category)