Research Article Subsolutions of Elliptic Operators in Divergence Form andApplication to Two-Phase Free Boundary Problems
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چکیده
Let L be a divergence form operator with Lipschitz continuous coefficients in a domain Ω, and let u be a continuous weak solution of Lu= 0 in {u = 0}. In this paper, we show that if φ satisfies a suitable differential inequality, then vφ(x)= supBφ(x)(x)u is a subsolution of Lu= 0 away from its zero set. We apply this result to prove C1,γ regularity of Lipschitz free boundaries in two-phase problems.
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تاریخ انتشار 2006