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MR1029856 35R35 (35B65 35J25 49J10)
Caffarelli, Luis A. A Harnack inequality approach to the regularity of free boundaries. III. Existence theory, compactness, and dependence on $X$. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), no. 4, 583–602 (1989).
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