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The obstacle problem for functions of least gradient

William P. ZiemerKevin Zumbrun — 1999

Mathematica Bohemica

For a given domain Ω n , we consider the variational problem of minimizing the L 1 -norm of the gradient on Ω of a function u with prescribed continuous boundary values and satisfying a continuous lower obstacle condition u ψ inside Ω . Under the assumption of strictly positive mean curvature of the boundary Ω , we show existence of a continuous solution, with Holder exponent half of that of data and obstacle. This generalizes previous results obtained for the unconstrained and double-obstacle problems. The...

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