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Part of the book series: Springer Theses ((Springer Theses))

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Abstract

In this chapter we study some properties of solutions to the problem (1.5). We first give an interior Hausdorff measure estimate of the free boundary of these solutions. Then we prove the uniqueness of the solution to (1.5), which then can be identified as the minimizer of a functional. Finally, we prove the uniqueness of solutions to the corresponding parabolic problem of (1.5).

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Wang, K. (2013). Uniqueness in the Singular Limit. In: Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33696-6_3

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