Partial Regularity For Weak Solutions Of A Nonlinear Elliptic Equation
For scalar non-linear elliptic equations, stationary solutions are defined to be critical points of a functional with respect to the variations of the domain. We consider u a weak positive solution of -DELTAu = u(alpha) in OMEGA subset-of R(n), which is stationary. We prove that the Hausdorff dimension of the singular set of u is less than n-2alpha-1/alpha+1, if alpha greater-than-or-equal-to n-2/n+2.
161–172
79
2
1993
Manuscripta Mathematica
F.Pacard