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The Dirichlet problem for a prescribed anisotropic mean curvature equation: : existence, uniqueness and regularity of solutions

Abstract : We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation −div(∇u/1+|∇u|2)=−au+b/1+|∇u|2, where a,b>0 are given parameters and Ω is a bounded Lipschitz domain in RN. This equation appears in the modeling theory of capillarity phenomena for compressible fluids and in the description of the geometry of the human cornea.
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Submitted on : Tuesday, February 9, 2021 - 11:45:28 AM
Last modification on : Saturday, October 9, 2021 - 3:15:38 AM

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Chiara Corsato, Colette de Coster, Pierpaolo Omari. The Dirichlet problem for a prescribed anisotropic mean curvature equation: : existence, uniqueness and regularity of solutions. Journal of Differential Equations, Elsevier, 2016, 260 (5), pp.4572-4618. ⟨10.1016/j.jde.2015.11.024⟩. ⟨hal-03135815⟩

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