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For a given domain , we consider the variational problem of minimizing the -norm of the gradient on of a function with prescribed continuous boundary values and satisfying a continuous lower obstacle condition inside . Under the assumption of strictly positive mean curvature of the boundary , 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...
For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.
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