The nonhomogeneous minimal surface equation involving a measure (Q1891204)
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scientific article; zbMATH DE number 759258
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The nonhomogeneous minimal surface equation involving a measure |
scientific article; zbMATH DE number 759258 |
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The nonhomogeneous minimal surface equation involving a measure (English)
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29 August 1995
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We find existence of a minimum in BV for the variational problem associated with \(\text{div } A(Du)+ \mu= 0\), where \(A\) is a mean curvature type operator and \(\mu\) a nonnegative measure satisfying a suitable growth condition. We then show a local \(L^ \infty\) estimate for the minimum. A similar local \(L^ \infty\) estimate is shown for sub- solutions that are Sobolev rather than BV.
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minimal surface equation
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variational solution
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nonlinear elliptic partial differential equations
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local bound solution
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