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- W1511208511 abstract "The monotonicity theorem of Alt, Caffarelli, and Friedman [ACF, Lemma 5.1] plays a central role in the existence and regularity theory of two-phase free boundary problems. It has been extended, for example, to variable coefficient operators [C3, Lemma 1] and to eigenvalue problems [FL]. In this paper we reformulate the theorem so that it applies to inhomogeneous equations in which the right-hand side of the equation need not vanish at the free boundary. Of particular interest is the case in which Au takes two different constant values on the set where u > 0 and on the set where u < 0. The Prandtl-Batchelor" @default.
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- W1511208511 date "2002-03-01" @default.
- W1511208511 modified "2023-10-06" @default.
- W1511208511 title "Some New Monotonicity Theorems with Applications to Free Boundary Problems" @default.
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- W1511208511 doi "https://doi.org/10.2307/3062121" @default.
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