The Dirichlet problem for a prescribed mean curvature equation
نویسندگان
چکیده
منابع مشابه
On the Dirichlet problem for the prescribed mean curvature equation over general domains
We study and solve the Dirichlet problem for graphs of prescribed mean curvature in R over general domains Ω without requiring a mean convexity assumption. By using pieces of nodoids as barriers we first give sufficient conditions for the solvability in case of zero boundary values. Applying a result by Schulz and Williams we can then also solve the Dirichlet problem for boundary values satisfy...
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The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end along a line segment. The condition on the existence of these hypersurfaces is the vanishing of the sum of certain integral moments of the spheres with respe...
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It is known that for the parametric Plateau’s problem, weak solutions can be obtained as critical points of a functional (see [2, 6, 7, 8, 10, 11]). The nonparametric case has been studied for H = H(x,y) (and generally H = H(x1, . . . ,xn) for hypersurfaces in Rn+1) by Gilbarg, Trudinger, Simon, and Serrin, among other authors. It has been proved [5] that there exists a solution for any smooth ...
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ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 2020
ISSN: 0018-2079
DOI: 10.32917/hmj/1607396492