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MR1087186 (92m:35279) 35R35 (35B65 35J35 49N60)
Laurence, Peter; Stredulinsky, Edward Existence of regular solutions with convex levels for semilinear elliptic equations with nonmonotone $L\sp 1$ nonlinearities. I. An approximating free boundary problem. Indiana Univ. Math. J. 39 (1990), no. 4, 1081--1114.
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