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The nonhomogeneous
minimal surface equation involving a measure
William Karl Ziemer |
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Vol. 167 (1995), No. 1, 183–200
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Abstract |
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We find existence of a minimum in BV for the variational problem associated with div A(Du) + μ = 0, where A is a mean curvature type operator and μ a nonnegative measure satisfying a suitable growth condition. We then show a local L∞ estimate for the minimum. A similar local L∞ estimate is shown for sub-solutions that are Sobolev rather than BV . |
Mathematical Subject Classification 2000
Primary: 35J60
Secondary: 35D99, 49Q05, 58E12
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Milestones
Received: 13 August 1992
Revised: 13 January 1993
Published: 1 January 1995
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Authors |
| William Karl Ziemer | |
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