Abstract
In this paper, we show that, given appropriate boundary data, the free boundaries of minimizers of functionals of type J(v;A,\lambda_+,\lambda_-,\Omega)=\int_{\Omega} ( \langle A(x)\nabla v,\nabla v \rangle + \Lambda(v))\,dx and the fixed boundary touch each other in a tangential fashion. We extend the results of Karakhanyan, Kenig, and Shahgholian [Calc. Var. Partial Differential Equations 28 (2007), 15–31] to the case of variable coefficients. We prove this result via classification of the global profiles, as per Karakhanyan, Kenig, and Shahgholian [Calc. Var. Partial Differential Equations 28 (2007), 15–31].
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