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Barriers and existence results: For a class of equations of mean curvature type

Journal Article


Abstract


  • Suppose ft is a bounded C-domain in [formula omitted]. We investigate the Dirichlet problem [formula omitted] in Ω. [formula omitted] on ∂Ω [formula omitted] 'for a large class of quasilinear non-uniformly elliptic equations including those of minimal surface or mean curvature type. It is shown that the smallness of ϕ in the Lipschitz- norm guarantees the solvability of the problem, even if ft does not satisfy curvature restrictions. Counterexamples show that the results obtained are sharp. © R. Oldenbourg Verlag, München 1987

Publication Date


  • 1987

Citation


  • Schulz, F., & Williams, G. (1987). Barriers and existence results: For a class of equations of mean curvature type. Analysis, 7(3-4), 359-374. doi:10.1524/anly.1987.7.34.359

Scopus Eid


  • 2-s2.0-0040575777

Web Of Science Accession Number


Start Page


  • 359

End Page


  • 374

Volume


  • 7

Issue


  • 3-4

Abstract


  • Suppose ft is a bounded C-domain in [formula omitted]. We investigate the Dirichlet problem [formula omitted] in Ω. [formula omitted] on ∂Ω [formula omitted] 'for a large class of quasilinear non-uniformly elliptic equations including those of minimal surface or mean curvature type. It is shown that the smallness of ϕ in the Lipschitz- norm guarantees the solvability of the problem, even if ft does not satisfy curvature restrictions. Counterexamples show that the results obtained are sharp. © R. Oldenbourg Verlag, München 1987

Publication Date


  • 1987

Citation


  • Schulz, F., & Williams, G. (1987). Barriers and existence results: For a class of equations of mean curvature type. Analysis, 7(3-4), 359-374. doi:10.1524/anly.1987.7.34.359

Scopus Eid


  • 2-s2.0-0040575777

Web Of Science Accession Number


Start Page


  • 359

End Page


  • 374

Volume


  • 7

Issue


  • 3-4