6533b838fe1ef96bd12a4573

RESEARCH PRODUCT

Hypersurfaces of prescribed mean curvature over obstacles

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Let ~2 be a bounded domain in the euclidean space IR", n-> 2, with Lipschitz boundary ~ . We shall consider surfaces which are graphs of functions u defined on f2 having prescribed mean curvature H=H(x, u) with the side condition that they should be bounded from below by an obstacle ~b. The case H = 0 (minimal surfaces) has been discussed in detail by several authors, compare [6, 7, 12, 13, 17, 18, 20, 21, 24] of the references. Tomi [-31] has also investigated parametric surfaces with variable H. More general variational problems with obstructions have been discussed in [-9] and [-10]. During the session on "Variationsrechnung", held from June 18th to June 24th, 1972 in Oberwolfach, Miranda showed that the functional