Obstacle Problems for Scalar Ginzburg-Landau Equations (Journal of Partial Differential Equations, 2004)
In this note, we establish some estimates of solutions of the scalar Ginzburg-Landau equation and other nonlinear Laplacian equation Δu = f(x, u). This will give an estimate of the Hausdorff dimension for the free boundary of the obstacle problem.
Keywords: Laplacian operator; obstacle problem; free boundary; positive solution