Functions of least gradient and BV functions
Minimal rearrangements of Sobolev functions.
The Wiener criterion and quasilinear uniformly elliptic equations
Jacobi fields and regularity of functions of least gradient
Minimal rearrangements of Sobolev functions
The obstacle problem for functions of least gradient
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...
Fine behavior of functions whose gradients are in an Orlicz space
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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