Obstacle Problems for Scalar Ginzburg-Landau Equations

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Abstract

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
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Obstacle Problems for Scalar Ginzburg-Landau Equations. (2004). Journal of Partial Differential Equations, 17(1), 49-56. https://www.global-sci.com/index.php/jpde/article/view/4017