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• W2963706726 startingPage "111538" @default.
• W2963706726 abstract "In this work we demonstrate that a class of some one and two phase free boundary problems can be recast as nonlocal parabolic equations on a submanifold. The canonical examples would be one-phase Hele Shaw flow, as well as its two-phase analog. We also treat nonlinear versions of both one and two phase problems. In the special class of free boundaries that are graphs over Rd, we give a precise characterization that shows their motion is equivalent to that of a solution of a nonlocal (fractional), nonlinear parabolic equation for functions on Rd. Our main observation is that the free boundary condition defines a nonlocal operator having what we call the Global Comparison Property. A consequence of the connection with nonlocal parabolic equations is that for free boundary problems arising from translation invariant elliptic operators in the positive and negative phases, one obtains, in a uniform treatment for all of the problems (one and two phase), a propagation of modulus of continuity for viscosity solutions of the free boundary flow." @default.
• W2963706726 created "2019-07-30" @default.
• W2963706726 creator A5004919774 @default.
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• W2963706726 date "2019-12-01" @default.
• W2963706726 modified "2023-10-16" @default.
• W2963706726 title "Some free boundary problems recast as nonlocal parabolic equations" @default.
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• W2963706726 doi "https://doi.org/10.1016/j.na.2019.05.019" @default.
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