Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems
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Let Open image in new window be a divergence form operator with Lipschitz continuous coefficients in a domain Open image in new window , and let Open image in new window be a continuous weak solution of Open image in new window in Open image in new window . In this paper, we show that if Open image in new window satisfies a suitable differential inequality, then Open image in new window is a subsolution of Open image in new window away from its zero set. We apply this result to prove Open image in new window regularity of Lipschitz free boundaries in two-phase problems.
KeywordsDifferential Equation Partial Differential Equation Ordinary Differential Equation Weak Solution Functional Equation
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